Cutter and cutting method

Chips produced from an object being cut are prevented from adhering to the pieces that are already cut. A suction jig (6) for applying suction to a resin-sealed body (1) to be cut includes, on an upper surface thereof, a plurality of grooves (13, 14) that respectively coincide with a plurality of lattice-like boundaries (4) between regions (5) provided in the resin-sealed body (1). When a rotary blade (17) cuts the resin-sealed body (1) along a cutting line (20), the peripheral edge of the rotary blade (17) is received in a groove (21) in a cutting area, the groove (21) coinciding with the cutting line (20). A cleaning liquid (23) is ejected from a cleaning water nozzle (22) disposed in front of the suction jig (6) toward the groove (21) in the direction (-Y) in which the groove (21) extends and in which cut chips are discharged. The cleaning liquid (23) is also ejected from another cleaning water nozzle (24) disposed in front of the suction jig (6) in the -Y direction toward a groove (26) that coincides with