You need to check local law, but I doubt he has grounds for eviction based on your brief statement. He MAY be able to charge you for the plumbing calls though!
It really depends on the physical layout of the system, and exactly where the back-up is happening. He may have a collapsed or offset main that is creating a bottleneck that gets stopped up easily. Even so, the only thing that any tenant SHOULD put down the toilet is toilet tissue...nothing else! If it is YOUR toilet that is overflowing, it will be easy to prove you are the one clogging it. If it is farther down the line, or in the basement at a floordrain, then it would be hard for him to prove you caused it. He can have a camera run down the line to see exactly where the problem is, and if there is a consistent buildup, or a root problem, he should run a cutter blade down the line all the way to the street or septic tank to open it properly. Most cash-and-dash plumbers only push a drop head through, which just pokes a hole through the gunk, and does nothing for a root problem. A cutter will clear a much wider cross section, and allow better flow for the longer term, assuming the pipes are physically ok otherwise.