Cells with in vitro properties similar to those of bone marrow stromal stem cells are present in tooth pulp as quiescent cells that are mobilized by damage. These dental pulp stem cells (DPSCs) respond to damage by stimulating proliferation and differentiation into odontoblast-like cells that form dentine to repair the damage. In continuously growing mouse incisors, tissue at the incisor tips is continuously being damaged by the shearing action between the upper and lower teeth acting to self-sharpen the tips. We investigated mouse incisor tips as a model for the role of DPSCs in a continuous natural repair/regeneration process. We show that the pulp at the incisor tip is composed of a disorganized mass of mineralized tissue produced by odontoblast-like cells. These cells become embedded into the mineralized tissue that is rapidly formed and then lost during feeding. Tetracycline labeling not only revealed the expected incorporation into newly synthesized dentine formation of the incisor but also a zone covering the pulp cavity at the tips of the incisors that is mineralized very rapidly. This tissue was dentine-like but had a significantly lower mineral content than dentine as determined by Raman spectroscopy. The mineral was more crystalline than dentine, indicative of small, defect-free mineral particles. To identify the origin of cells responsible for deposition of this mineralized tissue, we genetically labeled perivascular cells by crossing NG2(ERT2) Cre and Nestin Cre mice with reporter mice. A large number of pericyte-derived cells were visible in the pulp of incisor tips with some having elongated, odontoblast-like shapes. These results show that in mouse incisors, rapid, continuous mineralization occurs at the tip to seal off the pulp tissue from the external environment. The mineral is formed by perivascular-derived cells that differentiate into cells expressing dentin sialo-phosphoprotein (DSPP) and produce a dentine-like material in a process that functions as continuous natural tissue regeneration.