aish.com answers it is permitted although ideally not with a metal tool
There is actually a custom not to cut tzitzit strings with metal.
There is a very interesting basis for this. The Torah states regarding
an altar that it must be made out of whole stones – ones which iron
was never “waved on” (Deuteronomy 27:5-6). The reason, as the Talmud
explains, is because iron is used to shorten the life of man (through
war), while an altar lengthens the life of man – by granting him
atonement before God (Mishna Middot 3:4).
Based on this, we do not use metal to cut tzitzit strings, since
fulfilling the mitzvah of tzitzit may also potentially lengthen a
On top of this, there are Kabbalistic reasons that the tzitzit should
only be cut with one’s teeth. Thus, ideally, you should shorten them
by biting off the ends. If this is difficult, however, it’s fine to
cut them via other methods – such as burning the ends or cutting them
with any non-metallic instrument, such as a ceramic knife.
(Note that however they’re cut, they should not be shortened down
beneath the required length – preferably about 11.5 inches).
(Sources: Rema to Shulchan Aruch O.C. 11:4, Magen Avraham 18 with
Machatzis HaShekel, Ta’amei HaMinhagim 19, Shulchan Aruch HaRav 11:24,
Kaf HaChaim 11:17, Mishna Berurah 11:61.)
See also further sources on this related MY question: Cutting tzitzis strings as well as here