To separate relatively long upright pipes (13) which have a relatively large diameter, the lower end thereof being fixed in the ground, in particular of support legs (3) of an off-shore oil bore or conveying platform (100), a cutting unit is lowered down into the pipe (13) to a separation point. The cutting unit (40) acts gradually from the inside across the periphery to the internal periphery of the pipe (13) and cuts through the pipe (13) by removing metal. A bore tool head (60) is mounted upstream of the cutting unit (40), viewed from the lowering position, and is used to bore out material in the pipe such as ocean bed or concrete.