The clutch face often becomes "stuck" to the compressor shaft due to corrosion. If you plan on reusing the clutch face and the pulley then DO NOT use a metal tool to pry them apart. This would scratch the clutch surfaces.
Try using a couple of wood shims placed 180 degrees from each other and wedge them between the surfaces to "pry" them apart. If this is done evenly, so as not to **** the face on the shaft, they will come apart.
There is a "special" puller made to extract the face from the shaft and you may be able to "rent" one from Auto Zone. It threads into the face center and a bolt is used to push against the center of the compressor shaft. These pullers are not universal, and are made for a specific series of compressors. So, be careful to determine that one you use is made for your compressor. (There are several different ones just for the Nippon Denso compressors).
Before you pull the clutch face check the gap and measure it. This will tell you how much thickness of the shim(s) is needs to be subtracted or added. When you replace the clutch face put a thin film of anti-sieze compount, or silicone grease, on the splines of the compressor shaft.
Historic note: In the old days all you had to have is a clutch puller for Ford, GM, AMC, and Chrysler. Now there are at least four different puller kits for Nippon Denso A/C clutch/compressors alone.
