remove = move away set aside = place nearby

I didn't understand mainly remove Remove means to delete

It's explained very clearly, with your example sentence, on this page: http://www.ldoceonline.com/dictionary/set_1 You could understand "to set" as meaning "to place".

What is the context please? Thanks, if it is cooking it just means to take the mushrooms and leave them on one side, (put them somewhere) until you need them later for the recipe.

Carefully remove the stems from the mushrooms, chop them finely, and set them aside.