Partially defrosting, then refreezing? OK, so we shouldn't refreeze meat once it's been defrosted.

But if I've partially defrosted meat, then popped it back in the freezer, is that safe? Specifically I'm thinking of sausages or steaks or chops, which may be frozen in groups. You might want to pull them out of the freezer for 30 mins to 1 hr, so they thaw just enough to loosen up to separate them, then put half back. Is this safe?

My question is ... is there a clean cut off point with defrosting after which it becomes unsafe to refreeze, or does it just get progressively more dangerous?
If you're unthawing them in your refrigerator (below 40 F), then you should be just fine. Most beasties don't reproduce at any significant rate below 40 F.

There isn't a clean cut off point because it depends entirely on the existing level of contamination present in your meat. 

You should be aware that repeated cycles of thaw/freeze will really damage the texture of your meat. The cells simply do not hold up to that.