So, when someone says cut to the chase they mean get to the point. Stop dancing around the topic and tell me directly! Other expressions with similar meanings are: tell it to me straight and stop beating around the bush.
Ann: Well, umm, you know things have been tough...
Bob: Yeah?
Ann: And we've fought alot and, umm...
Bob: Ann, tell it to me straight! Stop beating around the bush, just say what you have to say!
Ann: I'm breaking up with you!
-----------
Employee: Sir, I have something I'd like to ask you if you have a moment. You see, I've been working really hard lately and putting in a lot of overtime and...
Boss: Get to the point, I don't have all day.
Employee: Yes Sir, I'd like a raise.
Boss: Times are tough but you've been doing good work how does 5% sound?
Employee: Thank you very much Sir!
------------
You should cut to the chase when asking for something.
Any questions? Have a nice day,
Phil