Here is a roundup of the numerous points of friction between the pair during Tillerson's 14-month tenure -- on everything from North Korea to climate change:
Iran deal's future
Trump has blasted the 2015 Iran nuclear deal -- aimed at curbing Tehran's nuclear program and a landmark achievement of his predecessor Barack Obama -- as the "worst deal ever negotiated."
In January, he grudgingly signed sanctions waivers "for the last time" -- ensuring Washington will live up to its commitments for another 120 days. During that time, he wants Congress and European allies to come up with a new deal.
Tillerson, however, had argued for Trump to stand by allies who retained support for the accord.
"We got along actually quite well but we disagreed on things," Trump told reporters after announcing Tillerson's exit.
"When you look at the Iran deal, I thought it was terrible, he thought it was okay. I wanted to either break it or do something, he felt a little differently. So we were not really thinking the same."
To talk -- or not -- with Pyongyang
Following a day of talks with China's President Xi Jinping late last year, Tillerson said US officials were exploring channels of contact with Pyongyang amid sky-high tensions over North Korea's nuclear and missile tests.
But a day later, Trump bluntly dismissed Tillerson's efforts.
"I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man," Trump wrote on Twitter, referring to North Korean leader Kim Jong Un.
Last week, however, the world was stunned when Trump accepted an invitation to negotiate face-to-face with "Rocket Man" himself.
When the announcement was made at the White House, Tillerson was thousands of miles away -- seeking to smooth over relations with African nations Trump had reportedly dismissed as "shitholes."
Sidelined, from the Mideast to Mexico
Tillerson was said to have repeatedly complained about a perceived invasion of his territory by Trump's son-in-law and senior advisor Jared Kushner.
Kushner was gifted the responsibility of brokering peace between Israel and the Palestininians by his father-in-law, along with a role in steering US-Mexico and US-China relations.
Clash on climate
In June 2017, Trump stunned the world by declaring his intention to withdraw from the Paris climate accord. Missing from the audience during Trump's announcement, Tillerson was reportedly against the move.
"It's important that the US maintains its seat at the table about how to address the threat of climate change, which does require a global response," the former CEO of oil giant ExxonMobil had said during his confirmation hearings.
The day after Trump's decision, Tillerson insisted the United States remained committed to cutting carbon emissions, with or without the Paris pact.
And on white supremacy
Last August, when a young woman was killed in violence stemming from a white supremacist rally in Charlottesville, Virginia Trump sparked an uproar by suggesting both sides were at fault.
Soon afterward, Tillerson distanced himself from Trump's stance.
"We represent the American people, their commitment to freedom and to equal treatment to people the world over, and that message has never changed," Tillerson said.
"The president speaks for himself," he added.
Who's the smartest?
Fuelling talk of a serious falling out between the pair, Tillerson was reported late last year to have referred to Trump as a "moron" after a national security meeting a few months earlier.
Tillerson never fully denied the claim, which prompted the president -- seemingly stung -- to challenge his top diplomat to an IQ test.
"I think it's fake news," Trump said of Tillerson's reported insult. "But if he did that, I guess we'll have to compare IQ tests. And I can tell you who is going to win."
Press secretary Sarah Sanders defended the jibe and denied any rift, insisting Trump "made a joke, nothing more than that."
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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