Tearing to enable the sewing of two stitches: Shabbat 105a, 105a-b
Tearing in destructive anger: Shabbat 105b
Tearing in mourning, for someone for whom there is no mitzvah of Tearing Clothes in Mourning: Shabbat 105b
Tearing open the sealed collar of a shirt: Makkot 3b
Potentially Related Forms of Work
Application of Tearing in the Tabernacle: Shabbat 74b-75a