What English expression resembles the German "Tutor"?
Firstly, even in Germany there are different word for this. Besides Tutor there is also wissenschaftliche/studentische Hilfskraft, HiWi (short for Hilfswissenschaftler but has apparently different meanings in other contexts) or Übungsgrupperleiter, for example, and the usage of these words may even vary between different parts of the university and their usage among students/faculty/administration is not always consistent. 

However, I think the most widely used term in English speaking countries is TA (teaching assistant).