I carry a hammer handle for breaking it. I gotta disagree with JJ on the knot strength. I use a Snell, or a Palomar, and knot strength is not an issue. Most braids are underrated and break well above their advertised strength. I fish Sufix 832. Hands down the best braid I've used. Not the thinnest or the smoothest, but it's smooth enough, has great abrasion resistance, and handles great. That Gore fiber lives up to the advertising.
You could try braid to mono leader. You'll get better feel and the lack of stretch will give you better hooksets and more control over the fish, while still enabling you to break off easier when you need to. I sometimes use a leader when fishing deep snaggy stuff for this reason. I use a Crazy Alberto to connect the lines. With a little practice it's easy to tie, and I've never had one fail. The leader will either break at the Trilene knot, or somewhere between the knots.
The only thing I do different is when I come back out with the tag, I wrap it around one side of the loop twice. It won't budge once cinched good, and I cut the tags as close to flush with the ends of the knot as possible. That makes it come through the guides smoother than leaving even a little tag, especially on the mono end.