Why did David regret that he cut the garment?
Shochar Tov 7: He caused Sha'ul to lose the Mitzvah of Tzitzis temporarily. Avi ha'Ezri (1:161, citing Agada) - now it had three corners, and it was exempt 1 , so Sha'ul transgressed Kil'ayim (he had wool Techeles threads on a linen garment, without the Mitzvah). We infer that one may enter a privy to defecate while wearing a Talis. 2
Radak: Perhaps it is a sin to cut the king's garment. Even though Sha'ul pursued David, one must fear the king!
Malbim (5,6): David was unsure if Sha
I.e. David cut and rounded off the corner. We need not say that he cut off the Tzitzis! If he cut straight (on a diagonal), it now had five corners, and was obligated (Zevachim 18b)! Refer to 24:11:3:1*. However, in any case Sha'ul transgressed Kil'ayim, for threads on three corners do not fulfill the Mitzvah. (PF)
I do not see a source to permit with a Talis worn especially for Tefilah. Sha'ul wore his robe the entire day! (PF)