To give more liberty, freedom, to allow someone to do something that is not usually allowed, or to treat someone less severely than is usual, to ease the pressure upon, thus give some slack, to let someone relax, to stop pressuring. Example: -I'm going to cut you some slack. Because it's the last day of classes, we don't have to talk anything serious today. If you and your kids don't agree about their futures, cut them some slack - explain your views, but don't try to force them to agree. "Cut me some slack" is exactly as "Give me a break!" PS. This idiom is invented by the black people of the United States, bringing "Cut" and "Slack" together . Hope this helps.

Fire up

it usually means to give one some space or time. "cut me some slack" also carries the same meaning. e.g.""I wish my boss would cut me some slack. He’s always telling me what to do. Every hour, he comes by my desk to check on me. It’s like he doesn’t trust me to do the right thing."" Hope this helps.