In cutting a downhole pipe in proximity to a closure in the pipe, the pipe is first perforated. A perforating torch is positioned with a pipe in proximity to the closure. The perforating torch produces cutting fluids in a first radial direction and produces an opening in the pipe, which cutting fluids produce a reaction force opposite to the first radial direction. This reaction force drives the perforating torch into contact with the pipe, anchoring it against any pressure wave produced by the cutting fluids and reflected off of the closure. Once the pipe is opened, a cutting torch is operated to sever the pipe. Any pressure wave generated by the cutting torch is vented through the opening.