We calculate the mass and residue of the heavy spin-3/2 negative-parity baryons with single heavy bottom or charm quark by use of a two-point correlation function. We use the obtained results to investigate the diagonal radiative transitions among the baryons under consideration. In particular, we compute corresponding transition form factors via light cone QCD sum rules, which are then used to obtain the magnetic dipole moments of the heavy spin-3/2 negative-parity baryons. We remove the pollutions coming from the positive-parity spin-3/2 and positive/negative-parity spin-1/2 baryons by constructing sum rules for different Lorentz structures. We compare the results obtained with the existing theoretical predictions.