First, open up the book and find one side or the other where the end sheet (the paper lining the book cover and first page) may be separated a bit from the first page or the cover. In the picture below you will see a small gap. If there is none, you can push the cover back and forth a bit against the spine to create a bit of a gap, but do not do this so hard that you tear anything.
Below is an arrow pointing to the small gap. Along this is where we will cut.
Once you cut it, the cover will fall away from the book. There may be a bit of glue or backing paper, this can be easily torn away.
Now cut the paper on the remaining side.
You should be able to easily remove the headband (the cloth at the ends)
Now you can separate the signatures one by one. Be very careful here, otherwise you will tear the pages. Chip away the glue and/or cut the strings as necessary. With a little patience, they should be fairly easy to separate.
Now you can take each signature and cut off the raw messy end with your paper cutter. I like to clean the glue off first, just so that you don't have extra junk messing you up.
If you can't put the whole thing in your cutter, cut them apart in the middle and then you can do them in smaller batches.