Remember what the idiom cry me a river is? cut sb some slack has the same structure as it, that is, a double object structure. If it is misunderstood as an object-complement structure, then the whole meaning has changed. Its literal meaning is almost "submit some idle parts to someone", which is equivalent to cub some slack for sb, which can mean "make someone relieved, let someone go" and so on, meaning:
give additional freedom to someone
give someone a break
make some allowances for someone
allow a person to something that is usually not allowed
For example:
I know he is not up to the mark right now but let's cut him some slack. He's new to this environment and needs time to adjust.
I know he is incompetent now, but let's just let him breathe a sigh of relief. He just got used to this environment and it took time to adapt.
parsing: up to the mark means that it meets the standards and meets the requirements.
Teenagers have a mind of their own. It's best to cut them some slack and let them do what they are doing instead of enforcing things on them.
Teenagers have a mind of their own. It’s better to let them relax and let them do what they are doing, rather than force them to do it.
parsing:
1, slack is an uncountable noun, so here you use cut them some slack.
2, instead of The things or actions behind must be replaced, while the actions in instead need to be done.
Had he explained the situation to me, I would have cut him some slack and not have been so hard on him.
If he explained the situation to me, I would have cut him some slack and not have been so hard on him.
Analysis: This sentence is a subtitle tone, and the clause contains should, had, were or other auxiliary verbs. The subordinate conjunction can be omitted if, and the auxiliary verb, modal verb be or have are placed at the beginning of the sentence to form a partial inverted assembly.
I was really busy last week and couldn't finish the report. Cut me some slack and I'll do it by tomorrow.
I was really busy last week and couldn't finish the report. Let me go, I will do it tomorrow.