A spring-mass model arranged in a diamond structure—mechanical diamond—is analyzed in terms of topology in detail. We find that additional springs connecting the next-nearest-neighbor (NNN) pairs of mass points and the modulation of the mass parameters to the pristine mechanical diamond generate multiple pairs of Weyl points in the frequency dispersion. Evolution of the Weyl point positions in the Brillouin zone against the uniform outward tension is tracked and explained by the point group symmetry, especially tetrahedral symmetry of the NNN springs. Interestingly, a rapid transmutation of the monopole charges of the Weyl points occurs as the tension varies. We also show surface Fermi arcs in the case with anisotropy in the NNN springs.