What software do you have? Sometimes if you have a larger design, you can rotate it in your software until it fits the hoop.This doesn't work with all designs depending on the shape of it.
Not seeing the design it is hard to say if it can be split. Can you make a jpg of the design and post it? I wouldn't suggest trying to reduce the size I find applique and cutwork are fussy like fsl when you try that. The cutwork area may become too small to try and trim. I checked my cutwork designs and the largest I have is 5x7 so I can't even test it to see how it would work sorry. You can try and reduce the size to the 5x7 that you need and save it as a different name like "whatever resized" so you still have the original and then test stitch the resized one.