We present a novel construction of the super-Pauli-Lubanski pseudo-vector for 4D supersymmetry and show how it arises naturally from the spin-shell constraints in the supertwistor formulation of superparticle dynamics. We illustrate this result in the context of a simple classical action for a “superspinning particle” of superspin 1/2. We then use an Sl(2; K)Sl(2; K) -spinor formalism for K=R,C,HK=R,C,H to unify our 4D results with previous results for 3D and 6D.