
Willow C. answered 06/24/19
Seasoned college-level tutor specializing in English
I believe this can be attributed to the fact that would you "mind to" do something is repetitive. For example, the "normal" (as in most commonly used) construction of the phrase is "would you mind ()ing _____", as in:
"would you mind sweeping the floor?"
Which in this case, the verb in its present participle form sweep(ing), already gives the task at hand, so "mind to sweeping" is inappropriate because said subject would already know you want them to sweep. They don't need that extra "to", which interrupts the phrase unnecessarily with information that is not pivotal to understanding the task at hand.