Daniel Wood has the right of it, I'm not advocating for you to punish them just because. Make the world feel real, and in the real world, violence has consequences. Frequently unintended and sometimes dire ones.
But I also think Daniel and I are coming at things from slightly different directions. When he talks about following the MC agenda (being a fan of the characters and playing to find out), that advice is predicated on the idea that all your players are on-board and on the same page with what they want to get out of the game. If that's the case and if they make characters who relentlessly engage in violence for its own sake, then he's absolutely right - that's what our game is about and you run with it.
The huge caveat here is what to do if some of your players want more depth to the story and some just want to get their bang-bang on. If that is the case then you have a mismatch in expectations about the game, and that needs to be addressed out-of-game more or less right away. Be straight with your players and encourage them to be straight with each other.
I don't know who your players are or what their histories are, so in some sense it's hard to say. But it's important to keep in mind that just because someone plays a Gunlugger doesn't mean that they're going to blast everything at every opportunity. And further, eve if that is their first instinct, it doesn't mean it will ruin the story. Hell, half the time you can use it to drive the story (see above about making violence consequential).
For example, I recently played in a 7th Sea game. My character was a massive Ussuran mercenary (think kind of like a Russian Cossack) who had spent the last 20+ years fighting on both sides of the equivalent of the 30-Years War. As a result he was extremely pragmatic and direct. In that game system, PCs and NPCs alike are simply "taken out" of a fight, and it is up to the players to describe how. Most of the other PCs were "Big Damn Heroes," so they would knock guys out, or wound them but not mortally, or have them dragged away by their horse, or whatever. When I described how Nikolai "took out" an NPC it was always as no-frills, direct, and lethal as it could be. I'm talking downright brutal. But this was a guy who had lost friends and comrades to "defeated" foes along the way, and now took no chances. But (and here's the important part), I didn't go looking for trouble. Nikolai didn't start fights, he ended them. Quickly and efficiently. He was fiercely protective of the other PCs and very loyal to them. But when things got hairy he was very hard to control, and that in and of itself became an important plot point later on in the game.
You'll need to make the call based on how your particular player generally rolls, but don't assume that just because he or she is playing a Gunlugger that they'll "wreck" things as a matter of course.