It would be unusual for a saddle like this to be glued in (if that's one of the exceptions, it's going to be the devil of a job to remove it...). A tight fit is not even necessary, but over time the saddle may be just stubbornly stuck. Firstly, protect the guitar table with suitable towels or such. Next, you'll want a pair of wide-jawed nail-pulling pliers like these...
You might get a better grip on the saddle by wrapping masking tape over the sharp jaws; you don't really want to use so much force as to cut through the plastic. Needle-nose are too narrow, as you've found out. Wide jaws, and gentle 'persuasion' should get it out. Anything else would imply more sophisticated gear, such as a Dremel drill, and mill it out, but that would be best confided to a luthier. Try the pincers first, but be firmly gentle. Good luck with it.