Haxor is right that in classical logic, to negate the implication of "I think implies I am" would be "I think and I am not."
However in natural language, negating an implication means something different. If someone says "I think therefore I am" and another person says "That implication isn't true, I disagree with it", they're not saying "I think and I am not" but they are saying it's in principle possible for something to think and not exist.
The negation of an implication in normal language is often more like saying "those two things aren't related in that way".