#1 says that you can FINISH something. #2 says that you can HAVE something (a finished assignment). #2 puts the main idea of the sentence into an adjective ("finished"). #1 puts the main idea into a verb ("finish"). #1 is the superior sentence because it is best to put your main action into a verb, not an adjective. Other than that there is absolutely no difference. Both #1 and #2 leave open the possibility that someone else might do the job for you. When you make a statement like "I will paint my house tomorrow" people understand that you are probably not doing it yourself.

In the first example, you are saying that you will finish the assignment. To have something done, implies that you might ask somebody else to complete the task. This is not going to be the case with assignment. To have something done does not rule out the possibility that you will do it. The two examples have subtly different emphasis. 1 - Emphasises who will complete the task 2 - Emphasises that the assignment will be finished