Cutting a knot:
Cutting the sewing and knot of the tailor: Even if a collar had already been opened [after being made] but a professional [tailor] returned and sewed [the two sides of the collar] together in the way done by professionals, or if the professional tied it [in a way] that one is unable to untie it, then it is forbidden to cut the strings. However this [prohibition to cut an undoable knot] only refers to a knot tied by the professional prior to having finished making the clothing, being that then the cutting of the strings of this knot involves the [prohibition of doing a] “Finishing touch”. As this finalizes the work needed to be done to the clothing being that through doing so the clothing is now fit to be worn, while until this was done it was never yet fit to be worn, [and it is thus forbidden as] any [action] done which is the finishing stroke [of the making of the vessel] contains [the prohibition of] “Finishing Touch” as was explained in chapter 302 [Halacha 5]
Cutting the knot of the launderer: However other knots which were tied after the clothing had finished having its work done to it, such as the knots of the laundering or the strings of a cloak which have been tied and one is not able to undo, [then] it is permitted to cut them. Nevertheless, even so one may not be lenient [to cut it] in front of an ignoramus, and rather should do it privately.
By a knot made to last 7 days: If one is accustomed to only cut the strings [of the collar knot] upon changing the cloak from Shabbos to Shabbos , then it is forbidden to cut [the strings of the knot] just like it is forbidden to undo it [as explained in Halacha 1].
Summary: Cutting the strings of a knot:
Anytime it is permitted to open a knot on Shabbos one is likewise permitted to cut it. However one may not be lenient to cut it in front of an ignoramus, and rather should do it privately. [As well in a case that the rope attaches an item to the ground then the rope may not be torn even if one is allowed to untie the knot being that doing so involves the destroying prohibition.]
Anytime that the knot is forbidden to be undone, it is likewise forbidden to be cut.