I don't know what to do with the broken blue sutures of my blepharoplasty left under the skin?

My
opinion is that it is better to leave the suture. Probably it’s a prolene suture
which can stay under the skin for a very long time. If the blue color is not
evident, it does not create any problem. Usually, after a few months it gets
aboarded by the organism. When it happens you will see it and you can pull it
out. Obviously if it gets infected you have to visit your doctor, but infection
is very rare in these cases. Regarding the bruising usually it is gone after 15
days, but sometimes it takes some more time. In case it does not disappear after
3-4 weeks, you have to visit your doctor. I think you have to keep your contact
with your doctor and don’t be anxious.

It should be quite simple to remove the suture and shouldn't require a reoperation.  You should return to your surgeon who I am sure will easily remove it.

I would return to your surgeon and many times these are removed very simply. If you leave it in for an extended period you may see more inflammation at the incision site. Many times these sutures work themselves out to the surface and are easily removed.