The difference in these sentence?
The function of the knife from sentence 1 is only to cut apples?

1) Do you have a knife to cut the apple with?

2) Do you have a knife to cut the apple?

Question

The difference in these sentence? 
The function of the knife from sentence 1 is only to cut apples?

1) Do you have a knife to cut the apple with?

2) Do you have a knife to cut the apple?

Answer

The two sentences have identical meanings. 'With' is optional but not essential. Both mean the speaker wants a knife because they need to cut an apple. Any knife will do. There is no suggestion it must be a knife specifically designed for cutting apples.

Answer

no, in 1) the speaker just specifies the action, not limits the function of the knife