Is it possible to remove a cherry angioma spot from the eyelid? (Photo)

Thank you for your nice question and photo. Your hemangioma / cherry angioma of the upper eyelid can be removed with a cosmetic procedure performed under local anesthesia in the office. I perform this type of removal very commonly in my practice and have removed hundreds of these. 
You need to see an expert in cosmetic mole removal who is experienced in removing growths from the eyelids specifically. There is always a risk for scar, recurrence, pigment changes (darker/lighter/red) in the area treated, and possible need for additional procedures. But an expert should be able to remove your eyelid growth with minimal scarring and an appearance more pleasing than currently. Your eyelid growth require a surgeon, not laser or freezing or any other method if you want the best outcome. 
Please seek out a board certified, fellowship trained Oculofacial Plastic Surgeon or other doctor with extensive expertise in cosmetic facial mole/growth removal.  I have had patients travel from around the country to have me treat them for this kind of challenging removal - especially after they were turned away by dermatologists, general plastic surgeons, eye doctors and family doctors. My coordinators can conveniently arrange such a visit.  I have removed thousands of moles from around people's faces throughout my career and each presents its own challenges, risks for scar, etc. You can review my photos to explore your options -- all my results shown are unretouched, unphotoshopped photos! Costs can be reviewed on my website or with my coordinators.
Best of luck in your search.
Damon B. Chandler, MD
Harvard-Penn Trained Oculofacial Plastic Surgeon

Small lesions on eyelids such as the one in your photograph can usually be removed easily with local anaesthetic. Scarring on the upper eyelid is good in most people.I advise you to consult a suitably trained and experienced plastic surgeon.