Excise, remove as if by cutting; also, form or shape as if by cutting or carving. For example, Young children love cutting out pictures from magazines, or The first step is cutting out the dress pattern. The first usage dates from about 1400, the second from the mid-1500s.
Oust, replace, or supplant someone, as in He cut out all her other boyfriends. [Mid-1600s]
Also, cut out for. Suited or fitted by nature, as in Dean's not cut out for lexicography. [Mid-1600s]
Also, cut out for. Assigned beforehand, prepared, predetermined, as in We have our work cut out for us. [Early 1600s]
Deprive, as in He cut her out of his will. [Early 1800s]
Stop, cease, as in He cut out the motor, or Cut out that noise! [c. 1900] Also see cut it out.
Leave, especially in a hurry; also, run away. For example, I'm cutting out right now, or At the first hint of a police raid they cut out. [Slang; first half of 1800s] Also see cut and run; cut the comedy.