A safety razor includes a handle assembly elongated along a longitudinal axis, a blade head assembly pivotably connected to the handle assembly and having a first blade set thereon, the first blade set extending generally in parallel with the longitudinal axis. The blade head assembly can be releasably connected to the handle assembly to facilitate replacement. The blade head assembly can include a second blade set, the second blade set extending generally in parallel with the longitudinal axis, the first and second blade sets arranged facing away from each other such that the shaving direction of the blade head assembly can be altered by rotating the safety razor about the longitudinal axis. The safety razor can further include a biasing element for resisting pivotal motion of the blade assembly about the longitudinal axis and a control mechanism operable to selectively limit the pivotal motion of the blade head assembly.