I did some research but I struggled to find an exact origin of how Savage obtained his lightsaber. I know it is Sith tradition to steal one from a Jedi and "bleed" the crystal, but there's no allusion to this process taking place. Did Dooku just gift Savage a random lightsaber?
This is purely speculative, but I believe an answer can be found in the third season episode "Monster." In that episode, Savage uses a sort of spear to massacre the Republic and Separatist troops on Devaron. This includes Jedi Master Halsey and his Padawan, Knox. After that episode, it is not used again. My guess is that Savage took the lightsabers of Knox and Halsey and used them to create his own weapon. Although the bodies of the Jedi are brought to Coruscant by clone commandos in the next episode, the lightsabers are not present. Therefore, my belief is that the crystals in those weapons were bleed and used to make Oppress' double-bladed lightsaber.