Drain pimiento; pat dry with paper towels, and finely chop. Stir ground mustard and ground red pepper into flour. Gradually add chopped pimiento to flour mixture, tossing to coat.
Beat cheese, butter, and salt at medium speed with a heavy-duty electric stand mixer until blended. Gradually add flour mixture, beating just until combined.
Turn out onto a well-floured surface. Divide into 2 equal portions; flatten each into a square. Roll each square to 1/8-inch thickness. Cut with a 1 1/2-inch square cutter. Place 1 inch apart on parchment paper-lined baking sheets. Bake 15 to 20 minutes; cool on baking sheets on wire racks 30 minutes.