Do you mean the coupling on the mixer end or the jar(bowl) end?
If it is mixer end, and you have the replacement you could just use a pair of tin snips or garden shears to carefully break off bits till its all gone.
You're right it, does just push in, but age, heat and minute quantities of kitchen grease can cause it to grip like hell. If however you want to save the old coupling, you will have to disassemble the entire machine including the motor and then get a firm grip on the armature and try to pull it loose. Bit of a job, but the up side is that you get to clean up the innards as well. ;-)
If it is the bowl (jar) end, remember that its a left hand screw so you need to turn the coupling the "wrong" way. Its counter-intuitive but that's the way it is on all the bowl-end couplings (I think its to stop them from screwing loose while running)
Rumi, February 2014