You can destroy stuff by making the new "Obliterator". It costs 8x iron, 4x copper and a thunder stone which can be purchased from the vendor.

Regarding repairs, no you can't select what you're repairing, but it also doesn't cost any resources, so spam that button to your heart's content.

Edit: You could also just throw all of the stuff you don't want into the ocean or a pit, but it'll always be there... taunting you... ;)