I want to put new tzitzit on my talis katan. Can I cut off the old ones or do I need to unravel them?
You can cut off the old ones. It is best to put them in genizah afterwards.
There is a custom not to cut tzitzis strings with a metal blade, but rather to bite them off with one’s teeth. However, this custom applies specifically to the preparation of the tzitzis strings, or possibly even to their shortening, and does not appear to apply to cutting them off in order to replace the tzitzis.
The custom noted in the answer is mentioned by the Maharshal (glosses to Tur 11), Mateh Moshe, Shelah, Magen Avraham, Mishnah Berurah (11:61), and others.
As the Leket Hakemach Hachadash (11:23) points out, the custom does not have any source in the Talmud or any other writings of Chazal, and is based on a verse that prohibits raising an iron tool to hew the altar, which has no connection to tzitzis strings.
Nonetheless, the custom, as noted, is mentioned by poskim, and should be adhered to.
Yet, Beis Baruch (11:161) writes that the custom applies specifically to preparing the tzitzis strings, because these are strings that will be used for the mitzvah, and not to strings after they have already been tied. Kaf Hachaim (11:17) extends the application of the custom to shortening strings. Yet, it appears that the custom does not apply to cutting off stings entirely.