Get to the point - leaving out unnecessary preamble.
This originated in the US film industry. Many early silent films ended in chase sequences preceded by obligatory romantic storylines. The first reference to it dates back to that era, just after the first 'talkie' - The Jazz Singer, 1927. It is a script direction from Joseph Patrick McEvoy's novel Hollywood Girl, 1929:
"Jannings escapes... Cut to chase."
There's quite a distance from a single citation in a script direction to a phrase that is part of the language. It doesn't appear again in print for some years and we can be fairly sure that McEvoy wasn't the source of the figurative use of the phrase as we now know it.
That figurative use, i.e. the generalized 'get to the point' meaning emerged in the 1940s. The Winnipeg Free Press, March 1944 ran an article about screen writing that included this:
Miss [Helen] Deutsch has another motto, which had to do with the writing of cinematic drama. It also is on the wall where she cant miss seeing it, and it says: "When in doubt, cut to the chase."
That does imply getting to the point but isn't quite the current meaning as it relates specifically to film chases. The more general usage comes soon afterwards, for example, in this piece from the New England newspaper The Berkshire Evening Eagle, February 1947:
"Let's cut to the chase. There will be no tax relief this year."
The precept as it applies to films is as prevalent now as it was in the silent film days. Many, in fact it is not too strong to say most, films aimed at a young male audience involve plot devices that allow for car/boat/spacecraft chases. There is usually a token love interest storyline before everything in sight ends up in pieces.