Bad-Dying branch

One of the branches on my first plant seems to be dying or something.
It looks pretty bad. The bud is kind of softer than all the other branches buds and is kind of soft squishy. The stem is harder that all the others and its discolored. The base of the branch on the stalk is also discolored... see pic.
Should I or can I cut this one branch off? If I do cut it off will the rest of the plant stay good? If I leave it on will whatever is wrong with the bad branch spread to the rest of the plant?

cut it off, hang it and smoke it, and yes the rest of the plant will be just fine.

Thanks. If I cut it off should I cut it all the way where the branch meets the stalk? And do I leave the exposed part of the plant alone or should I put something over the cut spot?