From Longman Dictionary of Contemporary Englishcut the (umbilical) cordcut the (umbilical) cordDEPEND ON/RELY ONto stop being too dependent on someone, especially your parents → cut
Examples from the Corpus
cut the (umbilical) cord• Boys in particular need to cut the umbilical cord.• Before it could, I cut the cord and took it into the ante-room.• She would cut the cord that bound her to them cleanly and irrevocably. 