How to remove the Tzitzis from a Tallis:
In those cases in which it is permitted to remove Kosher Tzitzis from the Tallis, one is to untie the Tzitzis rather than cut them or tear them, and cause them to become invalid. [If, however, the strings are not Kosher then one may tear them off. Seemingly, however one is not to cut them off using a metal instrument, as explained in the next Halacha.]
Using a knife to cut Tzitzis strings: It is proper to beware not to cut Tzitzis using a knife. Rather one is to cut the strings using one’s teeth. [Thus, if one’s Tzitzis strings are long and one desires to shorten them, one is not to cut them using a knife.]
Is one to avoid using a knife even prior to entering the Tzitzis into the hole?
Is one to avoid using a knife even after the Tzitzis is already braided?
Is one to avoid using a knife even if the Tzitzis are invalid, or one is putting on a new pair?
Seemingly one is to avoid doing so. Vetzaruch Iyun.
May one use a non metal knife, such as a plastic knife?
One may do so in a time of need.
 Siddur Admur letter 31 in Raskin; Elya Raba 15:1 in name of Olas Tamid 15:2; P”M 15 A”A 1; M”Z 2
Other opinions: Some Poskim rule that if one is removing the Tzitzis in order to place nicer Tzitzis onto the garment, it is permitted to tear the Tzitzis off. [Levush as explained in P”M ibid; Mahariy Malko brought in Birkeiy Yosef 15:2; Poskim in Kaf Hachaim 15:9; M”B 15:3 in name of Chayeh Adam; see Tzitzis Halacha Lemaaseh 15:23]
 The reason: As one should not invalidate Kosher Tzitzis with his bare hands as doing so is a belittlement of the Mitzvah. [ibid]
 Implication of Admur in Siddur; Rav Raskin in Siddur footnote 168
 Admur 11:24; M”A 11:18; Mateh Moshe 13; Shelah Chulin; M”B 11:61
 The reason: This is based on the verse “Lo Sanif Aleihem Barzel etc” [Admur ibid] This verse states regarding the Mizbeiach that metal is not to be used on it, being that metal shortens the life of man, while the Mizbeiach lengthens the life of man. The same applies to Tzitzis through which one is blessed with a long life. [See Piskeiy Teshuvos 11:29]
 The reason: There are 32 teeth which correspond to the 32 strings. [Kitzur Shelah; Ben Ish Chaiy Lech Lecha 10; Kaf Hachaim 11:17]
 Implication of Admur ibid which writes this Halacha immediately after concluding in 11:23 that one is to cut the Tzitzis prior to entering it into the hole.
 Implication of Admur ibid; Kaf Hachaim 11:17
 Piskeiy Teshuvos 11:290