Accidentally cut through joist above eave
Without pictures it's hard to say. I don't fool around with structural (the cost of getting it wrong is too high) I'm going to assume you need to repair it.

What you'll want to do is called sistering. Basically, you'll take a new board the same size as the rafter (you said it was a 2x8 so get a 2x8) and use it to patch the damaged board. You'll need some 3"(or longer) nails or screws. I would also suggest some construction adhesive for added strength.


Attach the new board to the top part. Put the adhesive on and then attach it via nails/screws. Alternate locations and which side you're going from
Glue and nail/screw attach the lower (presumably smaller) part. This may take some clamping. Ensure it's as straight as you can make it.


Once dry, your joist should be as good as new