When people say SWIFT, they usually mean "international payments via correspondent banking". SWIFT is just a messaging layer to enable that.
Look into correspondent banking if you're curious how all of that works – SWIFT is just one (very popular) way correspondent banks can communicate with each other and/or look up paths to facilitate international payments for their account holders.
When I worked for JP Morgan 08-10, I used swift and after learning about it on college was very disappointed. It was just an email inbox where other banks/fi’s scanned in orders, trades, etc. think fax2email where the fax came over as a TIFF file. There was no metadata, ocr, or anything, I’d have to manually read the image file to get the account number dollar amounts etc to key in on a piece of proprietary custodian software. This meant there was also no way to parse the inbox. Looking for a specific transaction? Ask them when they sent it and read the hundreds of messages that came over within +/-5 minutes and hope they remembered the time right.
I always wondered about the security behind it, because it seemed like anything that hit our inbox that was a tiff and have a recognizable letterhead got acted on, no confirmations, 9-10 digit amounts were moving around based on that alone. Also Not sure that I saw the whole system or just a piece.
Not too familiar with that process, but as far as I understand, these routes (i.e. correspondent banks per currency/country and their reachability over settlement networks) are called "Standing Settlement Instructions". SWIFT does seem to offer these as a service [1].
But just like the messaging layer, this can be done via other means. For example, here [2] is Citibank Poland declaring their reachability for various currency transfers.
As for the messaging service itself, I believe that cutting off SWIFT SSI access would help in disrupting payment flows in the short term, but in the long term, sanction lists are the real enforcement mechanism.
As others in this thread have already said, these are a very powerful indirect stick when implemented as "you must adhere to our embargo lists, or we will prohibit all of the banks in our jurisdiction to do any kind of business with you, whether for embargoed clients or others".
Look into correspondent banking if you're curious how all of that works – SWIFT is just one (very popular) way correspondent banks can communicate with each other and/or look up paths to facilitate international payments for their account holders.