Cut something or somebody off (stop, separate or interrupt)

As he had not paid the bill, his electricity was cut off.

Cut through (take or be shortcut)

This path cuts through the woods.

Cut and run (to leave a place quickly to avoid being caught or detained)

When it became clear that he would get caught, he cut and run.

Cut both ways (to have both advantages and disadvantages)

Possessiveness in a relationship cuts both ways. (= It has both advantages and disadvantages.)

Cut loose (behave in an unrestrained way; break away from the influence of somebody)

At last, he realized that it was time to cut loose from his family. (= It was time to stop being influenced by his family.)

Cut your coat according to your cloth (not spend more money than you have)

If you don’t want to fall into the debt trap, you must cut your coat according to your cloth.

Cut somebody short (interrupt somebody who is speaking)

I tried to explain, but she cut me short.

Cut something short (Make something last for less time than planned)

We had to cut our trip short because Ann fell ill.

Not cut it (fall short of requirements or be unable to cope with a situation)

His usual excuses just don’t cut it with me.

Be cut out for (be suitable for)

He is not cut out for that sort of work.