Mini phlebectomy an option to remove large facial vein? (Photo)

I would not recommend phlebectomy as the 1st treatment choice in your case. There are multiple options for treating facial spider veins, so the most important thing is to go to an experienced Vein Specialist, who can evaluate you and determine what will work best in your particular case. Remember that this is a vein or vascular issue, and not a skin problem, so perhaps dermatologists are not the primary option. Facial veins such as these are very common, and are best treated very easily by superficial or topical laser. Treatment generally requires several sessions, although sometimes we are fortunate, and a single session will do. However, not just any laser will be effective, so you should be seen at an experienced office, who will use the right energy type for veins and not just treat your skin. There are several lasers which work extremely well on the face, including the 940 diode, the 1064 Nd-Yag, as well as ohmic thermolysis (VeinGogh or Veinwave). IPL or BBL light treatments are used by some, but these are not the best, or "gold standard" options. Injection sclerotherapy can also be done, although it is rarely necessary on the face. As a final option, yes - microphlebectomy can be performed, where the vein is actually removed through a tiny, needlestick incision under local anesthesia, but this is more invasive than the prior options, and is truly only a last resort maneuver. I recommend seeing a vein specialist who can offer several treatment options and can determine which is best for you.

Facial veins are tricky to treat. You definitely want an experienced phlebologist (vein doctor) to evaluate and treat. Some facial veins are effectively treated with sclerotherapy, while others can indeed be removed with phlebectomy. Necrosis isn't a concern as long as the treating physician ensures that they are treating a vein and not an artery. There is ample venous drainage through alternate channels, so (properly) closing or removing a vein rarely causes issues with blood supply to an area of the face.