We have imaged the Sunyaev-Zel'dovich (SZ) effect signals at 140 and 270 GHz toward 10 galaxy clusters with Bolocam and AzTEC/ASTE. We also used Planck data to constrain the signal at large angular scales, Herschel- SPIRE images to subtract the brightest galaxies that comprise the cosmic infrared background (CIB), Chandra imaging to map the electron temperature Te of the intra-cluster medium, and Hubble Space Telescope imaging to derive models of each galaxy cluster's mass density. The galaxy clusters gravitationally lens the background CIB, which produced an on-average reduction in brightness toward the galaxy clusters' centers after the brightest galaxies were subtracted. We corrected for this deficit, which was between 5% and 25% of the 270 GHz SZ effect signal within R 2500. Using the SZ effect measurements, along with the X-ray constraint on Te, we measured each galaxy cluster's average line of sight (LOS) velocity vz within R 2500, with a median per-cluster uncertainty of ±700 km s-1. We found an ensemble-mean < vz > of 430 ± 210 km s-1, and an intrinsic cluster-to-cluster scatter σint of 470 ± 340 km s-1. We also obtained maps of vz over each galaxy cluster's face with an angular resolution of 70". All four galaxy clusters previously identified as having a merger oriented along the LOS showed an excess variance in these maps at a significance of ≃2-4σ, indicating an internal vz rms of ≳1000 km s-1. None of the six galaxy clusters previously identified as relaxed or plane-of-sky mergers showed any such excess variance.