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.
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.
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.