Is it better to have a complete mole removal or partial removal over months?

I recommend getting a formal evaluation with a cosmetic dermatologist. Moles can be removed with laser, radiowave or shave. See an expert. Best, Dr. Emer

Removing a mole with several operations is usually called a serial excision. The reasons for using this approach are as follows: It may be the only way to  remove a mole in one go without using a skin graft to replace the area that has been removed.Serial excision may enable the surgeon to keep the scar shorter.Serial excision allows the surrounding tissue to stretch up to enable the mole to be replaced by the normal skin that surrounds the mole.You are best advised to seek the opinion of a suitably qualified and experienced plastic surgeon for their advice.Best wishes.

Without knowing about your mole specifically, here is information about moles in general.
If the mole is being removed because of concern that it may be atypical (medically suspicious), it is best to remove in its entirety, in one procedure, for two reasons:
1) If it is at risk of becoming cancerous, it should be removed earlier than later.  (Only after removal can you know with certainty if it was at risk, based on the pathologist's report).  
2) If it is removed in part, the scarring that will take place will change the tissue structure.  A second biopsy or removal (excision) can alarm the pathologist who reads the tissue slide, because it will look atypical.  This could result in higher concern and possibly the need for another procedure to take more skin around the mole (a margin).

If the mole is being removed for cosmetic purposes, there is no benefit to creating multiple small scars.  The exception would be if the mole is very large.  If so, after it is removed there will be a large wound, and there may not be enough skin around it to close with stitches (sutures).  If the mole is so large that this is a concern, see a plastic surgeon for consultation - perhaps even more than one surgeon.  It is your face after all!  
Lastly - if the only reason to remove it is cosmetic, think carefully about whether the scar would look better, in your opinion, than the mole.  Ask the surgeon how large the scar will be, and what shape.

Thank you for your question. The amount of treatments the mole removal takes depends on the size of the mole. Because the mole is on your face, a plastic surgeon will want to achieve the best scar possible. If the mole is large, and you remove the whole thing, closing it with sutures can become an issue, leaving a widened scar from too much tension on the incision, or an overall distorted appearance from pulling two edges together that were originally so far apart. I am assuming based on the information you've provided that's what the two doctors you've visited are considering. A complete answer for this would require an in-person consultation with a Board Certified Plastic Surgeon which it sounds like you've already done. I would recommend getting a second opinion from another BCPS who will move forward with excision. Good luck and best wishes!