The beauty of Jesus's grace is that even though all of us screw up and don't deserve, God still gave it via Jesus -- and he gave it abundantly! But with that said, that doesn't mean that doing sin is now a good idea!
Paul proclaims that hyper-abounding grace doesn't mean that sin is a good idea. In fact, Paul notes that we have "died to sin" and rhetorically asks how we can "live any longer in it" (6:2). Previously, we read how one of the side effects of sin is separation from God, resulting in death (since God is the life-provider). Some sins (like fostering violence) can also directly cause death!
Basically, there are various practical reasons why not to do sin (not just having a bad record to God).