Mutton snapper, especially the big ones, tend to be very spooky and slow to bite. Try to keep everything natural looking and all terminal tackle to the bare minimum when targeting tricky muttons. A slide rig is a great choice for mutton snapper as it allows you to "spool" out the bait.
"Spooling" is pretty simple.
1. Drop the bait down to the bottom. Try to go a little slow as this keeps your bait, sinker, and leader from tangling into one giant mess.
2. When the sinker hits the bottom you will feel a slight bump. Don't engage the reel, but instead continue to let the line flow back.
3. In a perfect world this allows the sinker to lay flat on the bottom and the bait is left floating with the current.
4. Pay close attention to the speed the line is going out. If it suddenly speeds up you have been picked up (If it's a mutton its very often a hard thump and a blazing runoff!)
5. When your picked up, engage the reel and start cranking. If using a circle hook just crank until the rod bends over and the fights on. If using j-hooks crank until the rod starts to bend over, give a quick hookset, and start fighting!
Good luck and good spooling!