To elaborate a little on my earlier comment: When it is decided to stop taking aspirin, it is not needed to taper off. (see brochure of aspirin)
I did not talk about whether it is a good decision to stop or not.
I agree with Flycaster305 that it would be best to talk to your doctor about your plan of stopping.
I'd pose the question to your doctor. Aspirin is a wonderful but potent drug, but I'd take anything but cautions with a grain of salt. Most of us aren't qualified to answer that question.
You can stop taking aspirin abruptly. No tapering off is needed. Of course, you should be aware that your arthritis could cause more discomfort without the anti-inflammation effect of the aspirin.