Is it permissible to cut ties of kinship with relatives who cause embarrassment and insult, knowing that Islam encourages maintaining kinship ties, and that maintaining them leads to a loss of dignity?

Kinship ties are religiously encouraged, not optional or a matter of reward. The true religion has urged their maintenance and forbidden their severance. It is sufficient as a warning against severing them that Allah Almighty has linked it with corruption in the earth in His saying: "(Then, is it to be expected of you, if ye were put in authority, that ye will do mischief in the land, and break your ties of k kith and kin?)" (Muhammad: 22). Whoever severs his kinship ties bears its sin, but this does not negate his right to be reunited with.