Cold inelastic collisions between confined cesium (Cs) atoms and Cs2 molecules are investigated inside a CO2 laser dipole trap. Inelastic atom-molecule collisions can be observed and measured with a rate coefficient of ∼ 2.5 × 10 −11 cm 3 s −1 , mainly independent of the molecular ro-vibrational state populated. Lifetimes of purely atomic and molecular samples are essentially limited by rest gas collisions. The pure molecular trap lifetime ranges 0,3-1 s, four times smaller than the atomic one, as is also observed in a pure magnetic trap. We give an estimation of the inelastic molecule-molecule collision rate to be ∼ 10 −11 cm 3 s −1 .