If you have matching pieces of fabric, you can hand applique a matching piece of fabric over the cut. This can end up being practically invisible.

Before doing that, you can insert a small piece of fusible underneath the cut edge and fuse the edges more or less together. That will strengthen the cut that is underneath the applique.

Can you slip a piece of fusible underneath the cuts and fuse the edges together? Are the cuts in parts of a pieced block? I had a seam blow out bad on a pinwheel quilt that I didn't find until after it had been quilted and washed. I just removed the offending piece with my seam ripper then replaced the piece and hand sewed it in. I did have to remove a little bit of the quilting but was able to re-sew it with my sewing machine. No one can tell the difference!