One possibility is remove.
gals
I am the word DOZENS (take away S and I'm dozen - meaning 12)
The answer is DRAW.
remote
remote
avoid
capture-meaning take away
The word you're looking for is "hate," which means to dislike very much. If you take away the letter "t" from "taste," you are left with "ase," which doesn't relate to the meaning. However, "hate" is a direct synonym for strong dislike.
evades
Solder.
Cart Cat At A
The 3-letter word for "sick" is "ill." If you take away one letter (the "i"), you are left with "ll," and by adding two letters (such as "a" and "s"), you can form the word "all."