His primary complaint is that the 2015 pact, which was originally conceived as a starting point for better relations between Iran and the West, doesn't extend beyond 2025.
He also criticized the deal for failing to address other concerns about Iran, such as its ballistic missile program or its support of the Lebanese militant group Hezbollah, its military aid of Syrian President Bashar al-Assad and its role in the war in Yemen.
Trump's stance echoes Israel's longstanding opposition to the deal. Israeli Prime Minister Benjamin Netanyahu last week alleged that "Iran lied" about its nuclear weapon ambitions in the 2000s, although the information he shared seemed to match up with what nuclear inspectors had already reported about Tehran's program.
Although Trump has been emphatic in his opposition to the deal, he was less clear about what should replace it or how far the U.S. is willing to go to limit Iran's nuclear ambitions or its regional aggression.
"With this decision, we should at least get some clarity on the White House position," said Sanam Vakil, a professor in the Middle East studies department at the Johns Hopkins School of Advanced International Studies in Bologna, Italy.
It also moves the Iran-U.S. tensions into a new phase after months of threats and insults. Iranian President Hassan Rouhani, who is considered a moderate,last month dismissed Trump as a "building constructor"with no understanding of law or international treaties.
What happens next?
Under the deal, formally known as the Joint Comprehensive Plan of Action (JCPOA), the United States committed to ease a series of sanctions on Iran and has done so under a string of "waivers" that effectively suspend them.
The waiver that was due for renewal on Saturday covers sanctions on Iran's central bank, intended to target its oil exports. Failure to renew the waiver means the sanctions will be restored, but under U.S. law the White House must wait 180 days before it can take action against businesses or nations that don't comply; this gives time for noncompliant transactions to be completed or wound down. Other waivers are due for renewal in July.
In his remarks on Tuesday, Trump said the United States would impose the "highest-level" economic sanctions on the Iranian regime.
Restoring sanctions amounts to a breach of the original deal. The JCPOA has a dispute resolution clause that would allow Iran to raise a complaint against the U.S. for violating its terms; that could buy time for more negotiation, but Trump's solid opposition to the deal means the dispute mechanism is unlikely to prove fruitful.
How will Iran respond?
While denouncing Trump's plan, Tehran has not been entirely clear about what it will do when sanctions return.
It could resume its nuclear arms program or step up its military involvement in Iraq, Syria, Yemen and Lebanon.
The secretary of Iran's Supreme National Security Council, Ali Shamkhani, warned last month that the country's Atomic Energy Organization was ready for some "surprising actions" if the deal failed — without elaborating — and said Iran was considering withdrawing from the Nuclear Non-Proliferation Treaty.
Iran says it has the technical ability to enrich uranium to a higher level than it could before the deal.
Rouhani has also ruled out any attempt to restrict its missiles, saying, "We will not negotiate with anyone about our weapons and defenses, and we will make and store as many weapons, facilities and missiles as we need."
If the deal is considered dead, Iran would no longer be obliged to allow international nuclear inspectors "so that we lose what visibility we have there," Rep. Mac Thornberry, R-Texas, predicted on "Fox News Sunday."
However, Iran appears to be in line with European powers who want the deal to continue regardless of U.S. involvement.
"Exceptional situations might occur at any time," Rouhani said before Trump's announcement on Tuesday. "These things happen in the world, but we will pass through this."
He added: "We may face some problems for two or three months, but we will manage the problem anyway. The basis of policy is to work with the world and have constructive engagement with the world."
The European Union's foreign policy chief, Federica Mogherini, said the deal is "a good and robust agreement that serves the interests of all parties."
And French Defense Minister Florence Parly said Tuesday that "we will need to keep pushing to defend the improvement of this deal, whether the United States is part of it or not."
However, a major hurdle for the remaining powers in the deal will be operating under a different sanctions policy than the U.S.; experts predict that most major international companies will comply with U.S. sanctions in order to protect their interests in the U.S. market. The more sanctions are restored by Washington, that harder it will be for Europe, Russia or China to keep the deal alive.
In Moscow, Russian President Vladimir Putin will have to respond to what his spokesman on Tuesday called a "very serious situation."
And while Iran's leaders may have been more willing to take a softer stance in talks with non-U.S. parties, anger at Trump's decision may make that politically impossible.
"Should there be some momentum, Iran has indicated that perhaps it might negotiate on some of the wider issues," Vakil said. "But right now it is obviously in a defensive mood, and domestic, sectional politics very much drives its ability to come back to the negotiating table."
What does America get?
The perceived benefit of restoring sanctions is that an economically weakened and isolated Iran would have to scale back its regional aggression.
"It also puts pressure on Iran and the international community to address Trump's personal concerns with the deal," Vakil said.
However, a simulation exercise carried out last fall by Israeli and American experts concluded that there was little else to be gained by scuttling the deal. In particular, it seems unlikely Iran would agree to a tougher deal while the international position is so divided; splintering the deal plays into Tehran's hands, the experts concluded.
What is Israel's view?
The collapse of the deal comes amid signs that Israel and Iran are moving closer to open warfare.
Netanyahu on Tuesday accused Iran of deploying "very dangerous weapons" in neighboring Syria. "It is now seeking to plant very dangerous weapons in Syria ... for the specific purpose of our destruction," he told reporters.
Israel has repeatedly warned it will not tolerate a lasting Iranian military presence in Syria, and is believed to have been behind recent airstrikes on Syrian military bases that killed Iranian soldiers, prompting Tehran to vow revenge. Israel has neither confirmed nor denied involvement.
Before Trump announced his decision, French President Emmanuel Macron had warned that war could ensue if Trump withdrew from the deal. Without limits on Iran's nuclear ambitions or inspections of Iranian facilities, Israel could feel compelled to act against its archenemy.
"We would open the Pandora's box. There could be war," Macron told the German weekly magazine Der Spiegel last month.
United Nations Secretary-GeneralAntonio Guterressaid last week that scrapping the Iran deal put the entire Middle East in a "very dangerous position."
After Trump's announcement on Tuesday, Macron tweeted that France, Germany, and the U.K. regretted the United States' decision but would work "collectively on a broader framework, covering nuclear activity, the post-2025 period, ballistic activity and stability in the Middle-East, notably Syria, Yemen and Iraq."
What will the impact be on America's reputation?
Perhaps the most troubling outcome of Trump's move for diplomats is the longer-term erosion of trust in the United States.
Iranian Vice President Eshaq Jahangiri said Tuesday that only "naïve" individuals would negotiate with the U.S. in the future. His comments echoed a warning from Rouhani that "no one will trust America again" after this episode.
It is something that might be noted by North Korea's Kim Jong Un as he prepares to sit down for talks with the U.S. following last month's summit that eased tensions with South Korea.
What are the implications for Iran?
The deal also has opponents in Iran, where many say they haven't seen the economic benefits that Rouhani promised would flow following the lifting of sanctions.
Spiraling inflation in Iran has fueled nationwide protests in December and January.
The collapse of the deal would also vindicate the position of Rouhani's hard-line opponents who criticized the very existence of any deal with the U.S.
That could drive Iran back into the hands of hard-liners in elections for its Parliament in 2020 and its presidency in 2021.
"The fallout from Trump's announcement will leave Rouhani completely marginalized," Vakil said. "Conservatives will have the dominant narrative, and Rouhani's legacy of engagement with the international community will be completely discredited."
Although Trump has been emphatic in his opposition to the deal, he has been less clear about what should replace it or how far the U.S. is willing to go to limit Iran's nuclear ambitions or its regional aggression.