Copper, and especially copper oxide, is a highly reactive material. This means that it pulls atoms from its environment to stabilize, including atoms from the cell walls of bacteria. Direct contact with cuprous oxide will weaken the cell wall, leading it to rupture and leak, killing the bacteria.
At the same time, the cell is programmed to draw in a certain amount of copper, but cannot balance this amount of copper fast enough, leading to an internal pressure that will cause the cell to burst, also leading to cell death. This level of copper is also toxic to the fragile DNA-making components of bacteria, causing interruptions in cell communication, energy absorption, and gene translation.