The invention is an implantable magnetic anastomosis device having an exoskeleton that directs self-assembly. The design allows the device to be delivered in a linear configuration using a minimally-invasive technique, such as endoscopy or laparoscopy, whereupon the device self-assembles into, e.g., a polygon. A coupled set of polygons define a circumscribed tissue that can be perforated, or the tissue can be allowed to naturally necrose and perforate. The device can be used to create anastomoses in a variety of tissues, such as tissues found in the gastrointestinal, renal/urinary, and reproductive tracts. New procedures for using anastomoses, e.g., surgical bypass are also disclosed.