出て行く is a compound word whose command form (命令形) is idiomatically used to tell someone to get out or get lost. Why not "出ろ"? Well, in similar contexts 出ろ would mean "get out", "leave", or "exit" without the rudeness and/or anger associated with 出て行け
For example, if I am having friends over for a house party and I all of a sudden smell gas, I would tell my friends to get out of the kitchen and maybe evacuate the house as well. 「出ろ」「出な」「出なさい」「出て」would work in that scenario. On the other hand if one of the friends gets drunk and is being a jerk to other people, I might tell them to 「出て行け！」.
It is interesting also to note that in English "Get out!" works in either scenario, but "Get out of my house/room/apartment/car/home!" only works in the second situation.