  We construct supersymmetric quantum mechanics in terms of two real
supercharges on noncommutative space in arbitrary dimensions. We obtain the
exact eigenspectra of the two and three dimensional noncommutative
superoscillators. We further show that a reduction in the phase-space occurs
for a critical surface in the space of parameters. At this critical surface,
the energy-spectrum of the bosonic sector is infinitely degenerate, while the
degeneracy in the spectrum of the fermionic sector gets enhanced by a factor of
two for each pair of reduced canonical coordinates. For the two dimensional
noncommutative `inverted superoscillator', we find exact eigenspectra with a
well-defined groundstate for certain regions in the parameter space, which have
no smooth limit to the ordinary commutative space.
