During a punchy vice-presidential dispute on Tuesday, Mr Pence was challenged to respond after Democratic Senator Tim Kaine argued that such remarks show Mr Trump's true colours.
"Senator, you've whipped out that Mexican thing again," said Mr Pence.
This did not go down well with Latin American viewers.
It escalated quickly with hundreds taking to Twitter to post their distaste at the comment using the hashtag #ThatMexicanThing.
Some of the posts were deliberately mocking of Mr Pence for displaying what was widely considered to be extremely poor judgment in making his remark.
Others made a point of highlighting the benefits of immigration in the US with many tweets featuring a sense of pride.
Mr Trump has made the fight against illegal immigration one of the main planks of his campaign.
He attempted to improve relations with Mexico by popping across the border for a few hours in a surprise visit in September.
But Mr Trump took the opportunity to defend the building of a wall between the two nations and despite referring to Mexicans as "amazing" and "spectacular", it was made clear that Mr Trump was not welcome.
Republican Governor Mike Pence has upset some in the Latin American community after he was asked in a live TV debate to defend Donald Trump's comments referring to Mexicans as "rapists" and "criminals".