In one aspect, the present disclosure is directed to a sheet material dispenser that includes a feed roller that is rotatable to facilitate dispensing of the sheet material from a discharge in a housing of the dispenser. The dispenser can have a cutting assembly that includes a cutting blade and at least one movable support coupled to cutting blade and that is actuated with rotation of the feed roller to cause movement of the cutting blade to at least partially cut, score, or perforate the sheet material during dispensing thereof. The dispenser also can have a biasing assembly coupled to the feed roller body to assist rotation of the feed roller body and/or movement of the cutting blade. Other aspects also are described.