Is a Punch Biopsy Enough for a Severe Dysplastic Mole?

A punch biopsy can be used as a tool for obtaining clear margins around a lesion depending on the size of the lesion and the size of the punch biopsy instrument. A shave biopsy is generally not going to obtain any sort of clear margins. The difference between 3 mm and 5 mm margins is very small and is going to be difficult to determine after excision/biopsy. Following up with your dermatologist and checking the area regularly would probably be the recommended course of action, but be sure to follow your doctor's advice.
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The lesion needs to be excised such that there are microsopically clear margins. Punch biopsy or elliptical excision are both acceptable methods of excision as long as the margins are clear.

Dysplastic nevi are atypical "funny looking" moles that are often categorized as having mild, moderate or severe atypia. They are generally larger and darker than other moles and have irregular or indistinct borders. When an abnormal mole is identified, a shave or punch biopsy is often performed for diagnosis. If the dysplastic nevus is classifed as severe, I often recommend a 5mm clear margin. In my experience, it is often difficult to clinically and pathologically distinguish these lesions from melanoma in situ.

A punch biopsy is enough only if it is VERY small.  A severely dysplastic mole is very close to melanoma.  I usually take at least a few millimeters margin to ensure the surrounding tissue is clear.  The pathology report should show how close the lesion was to the margin.  If it was close, I would recommend re-excision.

Atypical Nevi (moles) that are severely or moderately atypical need to be completely excised both clinically and microscopically.  Midly atypical nevi (sometimes called a Clark's Nevus) are considered, by most dermatologist, to be a variant of normal, and complete re-excision is not necessary.

A Biopsy Punch is really a tool that is generally used to obtain a diagnosis (biopsy) but this tool may also be used for treatment (excision).  Some Biopsy punches are large enough to encircle the entire lesion along with the necessary margin for clearance.  If the lesion is completely removed with adequate microscopic margins, you should be fine.

One thing to keep in mind-- the science of pigmented lesions is imperfect.  There is great debate within the scientific community about exactly what an atypical mole really means, about the necessity to treat and what the proper treatment is.   Be sure to consult with a respected, Board Certified Dermatologist that you trust and have a good rapport.  This is the best way to obtain your best care.