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 involving equivocation.
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.