Is it a tubeless tire? If so, it can be difficult to break the rim seal. It is sometimes possible to repair a tubeless tire without removing it from the rim by using a repair tool such as:
I made a tool for breaking difficult beads by grinding the sharp edges off a large flat blade screwdriver. By using a twisting action, you can gently work the blade between the tire and rim. Use caution to avoid damage.
My LBS's tech-trick that's worked dozens of times for me now (using screwdrivers etc have damaged beads and rims):
Place the rim on top of a preferably flat-lipped, plastic trash can (pic below).
With a little air still in the tube, press down on opposite sides of the tire using the bases of your thumbs and your weight for leverage.
Spin the wheel around to dislodge the whole bead, then do the other side.
I've found that it's easiest to remove a tight-fitting tire if the bead's broken on both sides of the rim, all the way around.