Would I be allowed to cut the tzitzis on a Tallis if they are fraying at the ends?
Yes you may cut them, however it should not be done with a metal knife etc. rather with one’s teeth or some other sharp material. The reason for this is that Tzitzis extends a person’s life (like a mizbayach) and metal shortens it, therefore we don’t use metal to cut them. The achroniim say the reason why specifically with the teeth is because we have 32 teeth and there ae 32strings of Tzitzis
Magen Avrohom 11-18, Machtzis Hashekel ibid, M”B siman 11-61, Shulchan Aruch Horav ibid 11- 24.