'치우다' means that you move a thing away from where it belonged.'지우다' and '삭제하다' are interchangeable in many ways. If anything, I could hardly find some cases that they are un-interchangeable. '지우다' is more colloquial, so if you use '삭제하다' too much, it would be awkward in many ways. For example, you can't say like "종이에 쓰여있는 것들을 지우개로 삭제했다". I suppose you could possibly use all three of them in a sense as equivalent English words.

If you have written something, you can 지우다 it. You can also erase a memory. Object you can see, you will 치우다 (snow, your room, obstacles). If you 치우다 something, the object still is there, but it is neat. If you delete 제거하다 something, the object seizes to exist (enemy, problems, tonsils).

Also refer to https://www.italki.com/question/441707