Synonyms for Cut into:

n.

shut off, kill off, suppress, interfere with, hold back, squeeze out, stamp out. top-slice, cut back, erode, reduce, trim down, decrease, minimize, shrivel, lower, halve. cut into (noun)
dig, delve, turn over.

v.

contact (verb)
dig, delve, turn over.

Other synonyms:

squeeze out, stamp out, kill off, suppress, interfere with, hold back. shut off.