If you have a washable filter, then yes, you can clean it and reuse it. If your filter is made of a cardboard frame with synthetic fibers, cotton, fiberglass, paper, then no, you cannot wash it or clean it. These are throw away filters.

Some air filters are washable. They are most often referred to as Permanent Electrostatic filters. Most of these washable filters use an aluminum frame, an aluminum or steel corrugated core sandwiched between a couple of layers of a polypropylene material, and an expanded metal support. In theory, the polypropylene develops an electrostatic charge as air moves through it. The electrostatic charge attracts the dust particles trapping them in the filter material.

Another washable filter is made of a rigid synthetic air filter media and regularly referred to as "Hog Hair Filters". The fibers are inter-weaved and bonded together to make a rigid self-supporting filter.

Both these types of filters are notoriously hard to clean after repeated use and cleaning. Particles get trapped to the point that they are nearly impossible to clean out. As time goes by, and with each washing the filter gets harder to clean 100% and eventually becomes a throw-away air filter. The hog hair filter will get progressively limp with each wash to the point that it will be impossible to slide into the filter track. Another thing to consider, or not, is whether you want to spent 30 to 60 minutes spraying the filter with a garden hose and having some of that water splashing on you. Oh, keep the vacuum cleaner in the closet or laundry room because unfortunately a vacuum cleaner will not do the job of cleaning the filter.