The expression works as its own antonym, so depending on the context it means:
1. To argue with
a powerful logic.
2. To make confusing arguments, usually
1. Man, you always
convince me! You are such a logic chopper!
2. No, we won't take the umbrella to the game. Just
because last year
it rained it doesn't mean this year
it will. Stop chopping logic. The weather forecast said clearly it won't rain
today. Enough said.