Publishing results that were trimmed from another paper
I suppose you could.  When submitting the paper with the "leftover" results, you'll probably want to explain in your cover letter what's going on, so that the editor doesn't think you're double-publishing those results.

However, I don't think it's a very good idea.  People usually expect a one-to-one correspondence between preprints and published papers.  Having results from a single preprint going in two separate papers will confuse people and make it harder for them to find and properly cite your work.  So if you are going to have two papers, I think you should have two preprints.

So first, decide how you are going to split up the results among papers.  Update the preprint of your current paper so that it matches the content (and title) that will be in its published version.  Then submit a new preprint with a new title containing the leftover results, corresponding to your second paper.

In your current paper, you can then cite the second preprint.