Moles, particularly ones found to be suspicious need to be excised with approximately 2 mm margin and submitted to a drmatopathologist for an examination.
The determination of whether a mole is benign or not is made by looking at all the areas of the mole including the outside edges and the deep portion. Shaving a mole off the surface of the skin is not adequate for either removal or examination. If the deeper or lateral components of the mole were not removed, it may recur. If there are positive margins (meaning there is some mole remaining) and the mole has been diagnosed as moderately or severely atypical, I recommend reexcision of the area to assure clear margins. If the mole is mildly atypical, I recommend watching for a recurrence then reexcising if it does.
We don't know yet what amount of risk do atypical or dysplatic moles carry in terms of becoming a melanoma. That remains to be determined. We do know that removing every single mole a person has is unnecessary and does not decrease the risk of a person developing a melanoma by very much. Melanomas start on normal skin more often that in a mole. So the moles that need toe removed are the ones that are suspicious for melanoma. We look for ABCDE (asymmetry, border irregularity, color irregularity, diameter greater than eraser of a pencil although many melanomas found early may be smaller than that, and evolution or any change in a mole).
Since this mole is recurring I would recommend reexcising it with conservative margins just to make sure it is completely removed.