We measure the rates of elastic and inelastic two-body collisions of cold spin-polarized neon atoms in the metastable
3P2 state for
20Ne and
22Ne in a magnetic trap. From particle loss, we determine the loss parameter of inelastic collisions $\ensuremath{\beta}=6.5(18)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for
20Ne and $\ensuremath{\beta}=1.2(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for
22Ne. These losses are caused by ionizing (i.e., Penning) collisions and occur less frequently than for unpolarized atoms. This proves the suppression of Penning ionization due to spin polarization. From cross-dimensional relaxation measurements, we obtain elastic scattering lengths of $a=\ensuremath{-}180(40){a}_{0}$ for
20Ne and $a=+{150}_{\ensuremath{-}50}^{+80}{a}_{0}$ for
22Ne, where
a0=0.0529 nm.