Your sentence is: "If I go shopping with you, I won't finish homework." It may cause a misunderstanding because "I won't (will not) finish my homework" may be interpreted as you making a choice not to finish your homework.
Therefore, we can make the meaning more specific by writing: "I won't be able to finish my homework." In this way, you would like to finish your homework but you weren't able to due to some reason.
Putting everything together, the sentence becomes: "If I go shopping with you, I won't be able to finish my homework."
Ps : I added "my" because I presume the homework is yours.
Hope this helps.