The noun "a release" is intended to formalise the process of releasing something into the public domain, so that it has a concrete sensibility - "a release" usually refers the the first version made public, but can also refer to "latest version", i.e. "latest release" of a piece of code, film, soundtrack, book, whatever. When the thing itself being released into the public domain has no actual physical substance (music, ideas, films) then there is a necessity to ground the language, and to do that you need a noun, so the verb "release" is changed into a noun.
It may be that in the context of the question, "a release" refers to the intial public release of a piece of software, even though there were many private versions. Instead of releasing the software then updating it, the actual release was held back - the compiler didn't have enough faith in the software to release it, but eventually decided to take the plunge and call it "a release" - i.e. a verson that functioned just enough that it was suitable of being released to the public, and then thought it was just like making a record, and wondering if people would like it, and felt like he or she had just "cut a record" and then changed "a record" to "a release".
If you reverse it: "to release a cut" it would work equally well to describe a different edit of a previously released film, hence the Director's Cut. Cut literally means the celluloid film "cut and spliced", here used metonymically, like "The Crown" for the state of Royal Sovereignty - "cut" means the film after editing: the cut.
The fact though, with "release a cut", is that in the film context "the cut" is a physical spool of plastic with coloured pictures on it, you can hold it, see it, carrying from one place to another, this is why the word "cut" works as a noun - metonynics, but it is right on the edge of tenuous.
But, to "cut a release" is not eytmologically derived from anything, all that is happening is the word order is being played with for the sake of novelty, so that it sounds different. People understand it because it is so hackneyed: it resonates both verb and noun as they can both be used in opposite ways in the same context - to release a cut, or to cut a release. The technical term to refer to this kind of use of English is nonsense - we know what it means but as soon as you scratch the surface it's meaningless.
It is someone trying to make something sound like a concrete thing about to happen, when there isn't actually a concrete thing happening. It is not metonymic because "a release" only refers the act of passing something from the private to the public domain, the thing itself doesn't change - a release isn't actually a physical thing like a crown, like a cut.
It could be that the person originally meant to "cut a leash" but was a drunk and it sounded like "cut a release" and someone else said,"hip dude".
To all intents and purposes it is just messing about with language and talking about something that doesn't exist in any material sense.
The problem with computer language and metaphors is the computer interface is itself a metaphor - so you can't do etymology on it. In the world of computers all metaphors work and you can sling two combinations together and find some answer for it. You can spend hours trying to find the root etymology, but it could equally be some neat expression coined by someone who made it up without any awareness of the history of the words he or she was using. Etymology is about a historical and cultural development of a word from a basic conceptual starting point - whereas computer language is just made up on the spur of the moment to attempt to define something that someone just made up. None of it exists except the tiny electrical pulses, in the silicon sliver.