Black/dark Brown Spot in Mole Biopsy Wound?

Since it's only been a short time since the biopsy, the most likely causes are persistence of nevus (mole) cells or char from the cautery instrument. When a pigmented lesion is removed by shave removal some nevus cells may be left behind (i.e. they're left in the wound because the doctor did not want to shave deeper and create an unacceptable scar). This can cause some residual pigmentation after the area has healed. Another option is that the cautery instrument caused some char of the tissue, and it appears black. In either case don't worry. See the doctor who performed the procedure and let them examine the site. Good luck.

Without a clear photo, it may not be wise to guess what the dark spot is.  It could simpley be a temporary mark from the cautery if one was used to burn the base of the growth in order to prevent bleeding post-operatively.  Instead of asking us to surmise, why not ask your surgeon?  This way, you will be sure!

Most likely this is a recurrent nevus. This is quite common with the shave technique. What occurs is that the top of the nevus was shaved off and now the nevus cells( the melanocytes) that are deeper, are exposed to the sun. The sun has activated these melanocytes and they are now producing melanin, the pigment that you see. 

There are two factors that weigh for benignity in your case: 1) the pigment recurred quickly and 2) the pigment is within the scar site.

Still, it would be important for you to bring this up with your dermatologist. He/She should then inquire of the dermatopathologist whether they are positive the mole is benign. In most cases, this reassurance is all that is necessary. However, if there is any atypicality or abnormality at all the mole should be excised in its entirely. 

It is also important that the dermatologist remind the pathologist that this is a re-exicion. The scar formation from the original biopsy can distort the pathology, making the specimen appear more ominous than it really is.

You most likely had a shave biopsy of your mole which typically leaves a minimal scar and sometimes will heal with a central area of hyperpigmentation. The mole will rarely regrow and the appearance with the central dark spot should not be objectionable. This is because the mole is actually "shaved off" at a level just below the surface of the skin. If the biopsy results show it to be cancerous or pre-cancerous then a second step, a complete excision with uninvolved margins, is necessary to ensure its complete removal.