Question 1 – Can you cut your tzitzit strings shorter?
Certainly. If you open the Shulchan Aruch to Orech Chaim 11, 4 you’ll see that the tzitzit are supposed to hang down at least 12 gudalim (thumb widths) and can be as long as you like. The Rema then writes, “And if one made it too long, you can shorten it…” one-third g’dil and one-third anaf. In laymen’s terms that means the knots and windings should be one-third of the total length, while the loose hanging section should be two-thirds. But if you buy a standard set of tzitzit strings and tie them according to the widespread custom, they will probably come out to about one-fourth and three-fourths.
I noticed that just about nobody seems to cut the tzitzis down to size, so I asked a rav. He said I can feel free to cut the tzitzit. “But I’d be the only one in town who cuts them to two-thirds/one-third,” I said.
“No, you won’t be the only one he said,” and pulled up his tzitzit from behind the desk and under his jacket – trimmed down to one-third/two-thirds.
Many tzitzit tie-ers have the custom never to cut tzitzit strings with scissors or any other metal object. Instead, any necessary cutting or shortening is done with one’s teeth (note that we have 32 teeth and 32 tzitzit strings hanging down), just as the Torah tells us that metal tools cannot be used to hew the stones for the Holy Temple. Like most professional tallit dealers, we use a pair of special zirconium oxide scissors to cut tzitzit when needed.
Question 2 – Can I cut off old tzitzit before I tie on new ones, or do I have to untie all the knots?
According to the Chayei Adam (11, 32), if untying the knots presents a difficulty or inconvenience, then you don’t have to untie your old tzitzits to make room for the new, but can cut them. What do you do with the worn tzitzis? It’s best to put them in shaimes, but not required. Just be sure to dispose of them in a respectful manner.