'to cut across' means to take a shortcut over an area instead of going around the edge.

• It'll be quicker to cut across the field.
• She quickly cut across the car park to where he was standing.

'to cut back' means to reduce the amount of money being spent.

• The government has cut back on education with less teachers.
• I've had to cut back on my spending as I'm not making any money at the moment.

'to cut down' means to remove a tree or plant by cutting it near the base.

• To make bigger fields, the farmer has cut down a lot of the hedges.
• We cut down the old tree in the garden as it blocked all the light.

'to cut down' also means to reduce the number or quantity of something.

• The article was too long and so I had to cut it down to fit the space.
• I have cut down the number of hours I work to only thirty a week now.

'to cut in' = to interrupt someone when they are speaking.

• I was trying to explain it when she cut in and started talking.
• He really annoys me. He's always cutting in and never lets me speak.

'to cut off' = to stop supplies of something like electricity or water

• They didn't pay the bills and the electricity was cut off.
• The water was cut off while they repaired the leaking pipes.

'to cut off' can also mean to stop a telephone connection.

• I'll ring him back. We got cut off in the middle of the conversation.
• I'm sorry but I pressed the wrong button and cut you off.

'to cut out' = when an engine or piece of machinery suddenly stops working

• There's a problem with my car. The engine keeps cutting out.
• When I stopped at the lights, the engine cut out.

'to cut through' difficulty means to be able to deal with the problems or bureaucracy quickly

• To get the permits in time, we had to find a way to cut through all the bureaucracy.
• She can cut through the complex legal language and get to the point.

'to cut up' = to divide something into smaller pieces

• It was too big to go into the bin so I cut it up.
• At the end, there was a cake left so we cut it up and each took a piece home.