A composite mandrel includes a filament-wound composite tube, and composite material molded over the filament-wound composite tube. For example, the composite material includes chopped fibers and a matrix of thermoset resin. The chopped fibers are arranged in layers upon the filament-wound composite tube, and the chopped fibers in each of the layers are randomly oriented along first and second orthogonal directions in each of the layers. The composite material includes at least one sheet of the composite material wound over the filament-wound tube, and at least one strip of the composite material wound over the sheet of the composite material and forming a head on the composite mandrel. An internal cavity of the filament-wound composite tube may provide a lumen for the composite mandrel. The internal cavity may be threaded to receive a removable bridge plug.