Effects of MHD reconnection events on the beam-plasma fusion reactivity and transport of the beam ions are studied. Based on the analysis of fusion reactivity changes induced by MHD events, the conclusion is drawn that the strong drops of the neutron yield during sawtooth crashes observed in the National Spherical Torus experiment (NSTX) are associated with both a particle redistribution inside the plasma and a loss of the beam ions. Mechanisms of the energetic ion transport during sawtooth crashes are analyzed, in particular, with the use of the resonance adiabatic invariant derived in this paper. A numerical simulation of the particle motion during a sawtooth crash in NSTX is done with the code OFSEF extended for a better description of the particle precession.