The present invention is generally directed to an interlocking modular mat or tile and method of use. The mat comprises a severable core structure with a ramp around its periphery and a connected outer structure. The outer structure surrounding the inner core structure is partitioned into side and corner panels also having ramps internally disposed therein. The novel features of the mat allows it to be cut along several locations to expose the internal ramp structure within each panel, providing a assembled mat system with a secure border around the entire mat. A method of constructing an array of the novel mat panel members involving cutting to expose the internal ramped structure is also disclosed to provide a flooring surface.