I am the original owner of a model 645, purchased approximately 25 years ago.

I ordered a replacement recoil spring. It is a factory original from Midway USA. However when I compare the two, the replacement is much longer. Like another 1/3rd longer. It is much harder to put in the gun, and with the replacement in, I cannot release the slide using the slide release lever.

Looking at the two, the coils of the spring are about the same size and wind at the same rate. Am I supposed to cut the replacement recoil spring to size, or just jam this spring that is 1/3rd longer into the gun and use it like that?

Are you sure they send you the right spring? Maybe using a one size fits all kind of thing? I know my 5906 spring fits six different models of guns and this could be the same thing.

Your old spring is well old, and if it has a lot of compression cycles it would have shrunk substantially.