You have to keep the entire phrase together to not lose the meaning. "cut straight to the solution" = "get to the point" i.e. stop discussing unimportant things

That sentence is strange because it starts off with "the cat" and ends with "the solution". "cut straight to the point" or "cut straight through the yard" mean different things. I picture a cat would cut straight through a yard (run really fast across the yard). In order for me to picture a cat cutting straight to a solution, the cat would have to be human-like. Like the cat was talking to me and the first thing it told me was the solution to a certain problem.