Wrap sweet potato in a paper towel. Microwave on high until soft, 4 minutes. Scoop flesh into a bowl and mash; set aside.
Heat oven to 400 degrees. Place biscuit mix and butter in a bowl; rub butter into mix with fingertips until large pea-sized crumbs form. Add sweet potato, butter-milk and allspice; mix until just combined.
Transfer dough onto a cookie sheet and form into a 12" x 4" rectangle. Cut into 8 rectangles with a serrated knife and separate slightly. Bake until biscuits are firm to the touch, 8 to 10 minutes. Transfer to a wire rack to cool. Once cool, store in an airtight container for up to 3 days.