Mergers of galaxy clusters are the most energetic events in the universe, driving shock and cold fronts, generating turbulence, and accelerating particles that create radio halos and relics. The galaxy cluster CL 0217+70 is a remarkable late stage merger, with a double peripheral radio relic and a giant radio halo. A Chandra study detects surface brightness edges that correspond to radio features within the halo. In this work, we present a study of this cluster with NuSTAR and Chandra data using spectro-imaging methods. The global temperature is found to be kT = 9.1 keV. We set an upper limit for the IC flux of ~2.7x10^(-12) erg s^(-1) cm^(-2), and a lower limit to the magnetic field of 0.08 microG. Our local IC search revealed a possibility that IC emission may be dominant at the outskirts of a radio halo emission and on/near shock regions within ~0.6 r500 of clusters. We detected a "hot spot" feature in our temperature map coincident a surface brightness edge, but our investigation on its origin is inconclusive. If the "hot spot" is the downstream of a shock, we set a lower limit of kT > 21 keV to the plasma, that corresponds to M~2. We found three shock fronts within 0.5 r500. Multiple weak shocks within the cluster center hint at an ongoing merger activity and continued feeding of the giant radio halo. CL 0217+70 is the only example hosting these secondary shocks in multiple form.