How Can I Remove Large Veins on Eyeballs?

Your eye veins will be best assess by an Opthamologist who has tools small enough to treat on the cornea and or sclera.

You need to see an opthamologist for this - they are eye doctors and are the only doctors who should touch an eyeball.  Good luck - Dr G
 

Veins on the eyeballs should only be treated by an eye specialist, an ophthalmologist. Cosmetic surgeons should not treat eye disease. 

Greetings Jen~

Large vessels, or any vessels, on the eye ball itself should be evaluated by an ophthalmologist or ophthalmic surgeon.  The eye is clearly a delicate area that you would want to avoid any complications so be sure to consult an expert.

Dr. Grant Stevens      

To treat any condition of the eyeball you should only be seen by an experienced eye doctor an Ophthalmologist!!!

A picture would be great to see for this, but any treatment involving the eye should be seen by an eye surgeon or ophthalmologist.  I could guess at a few conditions but you should probably just go see a specialist to get a formal and accurate diagnosis.

Cheers

If removal is even an option for these vessels, you should consider having this discussion with an experienced ophthalmologist.