It is possible that your garden pruners or loppers could be spreading diseases from plant to plant in between pruning.  However, with pruning at this time in the season when plants and most virus and bacteria are dormant, the risk is minimal.  If you are cutting within the warmer seasons, when both plants and diseases are actively growing, the percentage increases in the spreading of harmful pests.  Sometimes it is hard to tell if a plant is infected, so if you want to be on the safe side, dip your shears in a 10% bleach solution before going to the next plant.