Is it permissible to boycott relatives who mistreat me and expose me to harm, limiting interaction to visiting them only on occasions and during illness?

If the situation is as described, then you are not severing ties of kinship; rather, they are the ones who are severing and mistreating. As long as you maintain connection with them to the best of your ability without harm befalling you, then you are upon immense goodness. As the Prophet, peace and blessings be upon him, said: "If you are as you say, then it is as if you are feeding them hot ashes, and there will always be a supporter from Allah against them as long as you remain in that state."

The Shari'ah does not specify a particular method for maintaining ties of kinship. Rather, the reference point for this is custom and varying circumstances. It is achieved through visiting, contacting, corresponding, and everything that custom considers a connection. Among the greatest forms of connection is enjoining them to good, forbidding them from evil, and inviting them to repentance. If they do not repent, there is no blame upon you for boycotting and abandoning them; in fact, abandonment may become obligatory if it is determined to be a means of reforming them.