Michael McFaul, who served as ambassador from 2012-14, said that Mr Trump's "flippant" remarks show he "does not understand diplomacy" and that "sarcasm doesn't work in foreign policy".
Commenting on the expulsion – seen as retaliation by the Kremlin for fresh US sanctions against Russia - Mr Trump expressed his gratitude to Mr Putin for business reasons, because the measure allowed the US to “cut down our payroll.”
“I want to thank him, because we’re trying to cut down our payroll, and as far as I’m concerned I’m very thankful that he let go of a large number of people because now we have a smaller payroll," Mr Trump told reporters at his Bedminster golf club in New Jersey.
Mr McFaul, now a professor at Stanford University, took the President to task on Twitter, and in his Washington Post column where he criticised the “flippant” comments and questioned the President’s true motivations for failing to condemn Russia.
It sometimes seems like Putin is the only politician in the world who Trump hasn't criticized. Who else is on that list? https://t.co/5Wc7F49rxt— Michael McFaul (@McFaul) August 11, 2017
"Trump just applauded cuts of 755 in Russian embassy. Maybe he should look to trim his own staff?" Mr McFaul said.
"You realise Mr President that the State Dept organises US delegations to GES [Global Entrepreneurship Summit] - those same people you just said were not needed in Russia. Our diplomats, professional staff, and military serving in Russia provide Washington with invaluable information about Russia," he continued over a series of tweets.
Imagine wanting to have less capability to gather data about dangerous transnational diseases originating in Russia!Trump seems to want that https://t.co/xTVOkVohre— Michael McFaul (@McFaul) August 10, 2017
"Imagine wanting to know less about Russia's military modernization! That's what Trump praised today. Imagine wanting to know less about Russian foreign policy intentions and plans!" Mr McFaul added.
"That's what embassy personnel reductions will do. Imagine dissing Americans —patriots serving our country under difficult conditions in Russia -to praise Putin. Our President did today."
That @realDonaldTrump praised Putin today for cutting 755 people from our embassy in Russia shows that he doesn't understand diplomacy.— Michael McFaul (@McFaul) August 10, 2017
He pointed out that it was important to have a sufficient official presence in addition to secret intelligence, saying: “A ‘spy’ is undercover. A diplomat is not.”
In a television interview with MSNBC, Mr McFaul explained that even if Mr Trump had intended his comment to be tongue-in-cheek, it was ill-advised because "sarcasm doesn't work in foreign policy".
Tensions between Moscow and Washington have increased markedly since the Russian annexation of Crimea from Ukraine as well as Mr Putin’s support for the Assad regime in Syria.
Trump just applauded cuts of 755 in Russian embassy. Maybe he should look to trim his own staff? https://t.co/KKF0tP0PL2— Michael McFaul (@McFaul) August 10, 2017
In a television interview, Mr Putin explained the Kremlin’s decision to axe the US diplomats by saying he had grown tired of waiting for relations between the two superpowers to improve.
"We've been waiting for quite a long time that maybe something would change for the better, we had hopes that the situation would change. But it looks like, it's not going to change in the near future.
“I decided that it is time for us to show that we will not leave anything unanswered," Mr Putin added.
The explanation offered for why the number expelled was set at 755 is that Russia wants the number of American diplomats in Russia to be exactly the same as the number of Russian diplomats in the United States.
Mr Trump initially expressed opposition to extra sanctions against Russia, but he agreed to sign the new measures into law once it became clear there was bipartisan support for them across both houses of Congress.
The investigation into the Trump team’s alleged ties with Russia is ongoing, with many critics expressing continued doubts as to whether the President can be trusted to act in the best interests of the country when it comes to dealing with its former Cold War enemy.
Mr McFaul said in the Washinton Post: “When Trump praises Putin for these reductions, what country’s interests is he advancing?”
He urged Mr Trump to “correct his mistake” by negotiating with Mr Putin for a smaller reduction in the number of diplomats, or to respond with “some act of retaliation, such as closing down a Russian consulate”, which he said would “save Putin some money”.