Dont pry on the grill. You will pop it off the door panel and you wont be able to get it back on. It has plastic studs that are melted to the back of the door panel. It only takes about 5 minutes to remove the door panel anyway.
remove the phillips screw at the front and rear of the arm rest, pop out the 2 plastic plugs and remove the lagger screws under and then remove the screw holding in the window and lock switches. Work the switch plate through the opening in the arm rest and lift the arm rest off the panel. Remove the little triangle piece up where the mirror is and then the plastic cup around the door handle. There is one screw also at the bottom of the speaker grill, dont forget that one. Then just use a panel popper or your fingers if you dont have a popper, and work your way around the back of the panel pulling the plastic clips out of the sheetmetal. Once those are free it will lift right up and off. Its less work than it looks like.
You may not even have speakers in the doos, some LX's do and some dont depending on what stereo it came with. Once the panel is off the rest is self explanitory.
I have done many speaker installations in mustangs and the only speaker I have found to this day that is a drop in install and will fit under the factory grill is the Infinity reference 6.5's, The shallow mount ones. As big as mustang doors are, there is less than 2" mounting depth and the hole is a goofball size. Its not a 5.25" or 6.5", more like a 6" than anything. If you dont mind trimming metal and your speaker grills or building custom pods or buildouts then your options are pretty unlimited. But since you wanted to pry your speakers off I assume you arent wanting to go through that much trouble.
Another thing I just thought about...Two of the LX's I have didnt have speakers in the door from the factory and there were no wires for them either. If you have one without the factory speakers, you will have to run wires through the rubber boots in the door jam. It can be a pain in the ass and will be the most time consuming part of the whole deal. Also...dont bother with the dash speakers, just unhook or remove them altogether after you install decent door speakers. Trust me, it will sound better without them.