No. The mats have a Ground Fault Circuit Interrupter (GFCI) below the plug. This GFCI will instantaneously shut off all power to the mat if it detects a current leakage of more than 6mA.
Therefore, should there ever be a cut in the mat that could potentially cause harm, the GFCI will immediately detect it and shut off all power to the mat.
Additionally, all HeatTrak products are tested and approved to the UL standard 499, and carry the mark of the TUV.