There is also the possibility that what you have is a coil stamp, some of which have trimmed or no perforations on one or both sides.
For example this Southern Rhodesia coil stamp from 1929 - SG2c imperforate on the left.

Or this pair, Union of South Africa from 1914 - SG19 imperforate on both sides.

So, in fact the stamp may not be damaged at all but until you upload a scan it is only guessing.
Clive