  We prepare mixtures of ultracold $^{39}$K atoms in various hyperfine spin
states and $^{23}$Na$^{39}$K molecules in an optical dipole trap at a fixed
magnetic field and study inelastic two-body atom-molecule collisions. We
observe atom-molecule losses that are hyperfine dependent with a two-body loss
rate far below the universal limit. We analyze the two-body loss dynamics based
on the derivation of general and easy applicable analytic solutions for the
differential equations describing the loss of an arbitrary number $\gamma$ of
particles in a single collisional event.
