The steady magnetohydrodynamic laminar flow of an electrically conducting fluid on a radially stretchable rotating disk in the presence of a uniform vertical magnetic field is the subject of the present paper. The problem is an extension of the well-known von Karman viscous pump problem to the configuration with a stretchable rotating disk placed in inertial and/or noninertial frames (where a Bodewadt-Hartmann layer forms). The governing equations of motion are reduced to a set of nonlinear differential equations by means of conventional similarity transformations. An energy equation accounts for the viscous dissipation and joule heating terms. Employing a highly accurate spectral numerical integration scheme, the effects of a parameter based on wall stretching are examined in both frames. The quantities of particular physical interest, such as the torque, the wall shear stresses, the vertical suction velocity, and the rate of heat transfer, are calculated and discussed. It is found that the influence of the frame diminishes in the large limit of disk stretching.