Riding lawn mower tires have a reputation of being notoriously difficult to remove. Lawn mower tires that have been on for a while have a tendency to get stuck. When the bead of the tire--the section that comes in contact with the lip of the rim--gets stuck to the rim, it can be difficult to remove. However, with a few key tools and a little patience the job isn't too difficult.
Park the riding lawn mower on a level surface.
Jack up the riding mower. Place the jack under the tire that you intend to remove and raise the tire so that it is a few inches off the ground.
Remove the rim and tire from the axle or spindle. The method and tools required to do this vary greatly from model to model. Front wheel riding lawn mower tires are often affixed with an axle or spindle cap, which can simply be pulled off to expose a C-clip ring (to remove a stubborn C-clip ring, squeeze the clip with a pair of needle nose pliers and pull); and washers, which are also easily pulled off. Most rear wheel tires are affixed with a series of bolts (which can be removed with a wrench) and an axle key (which came with your riding mower and should be inserted into the hub of the tire). If you are unsure how to approach this, read your owner's manual, download one online, or contact the manufacturer for further details.
Release the air from the tire. Press the screwdriver against the valve until all of the air escapes the tire.
Remove the tire from the rim. Place the rim on the ground, with the outside of the rim facing up. Free the bead of the tire from the lip of the rim by wedging your screwdriver between the lip of the rim and the bead of the tire (take care not to damage the tire or the rim) and pressing down. Move the screwdriver all around one side of the tire and then move to the other side to free that one. After that, removing the tire should be as easy as pulling one side of the bead over the lip of the rim followed by the other.