Roses are heartier plants than they often get the reputation for and the most direct route to killing them is to deny the plant and roots any ability to manufacture nutrients via photosynthesis or absorb water and nutrients from the soil. This can be achieved with drastic pruning and then excavation of the roots from the planting soil.
Cut off all the above-ground rose canes down to the crown of the plant with loppers. Gather the cuttings from the soil surface and compost or discard them.
Dig around the root ball of the rose with your shovel or spade to expose the crown and main root mass of the rose. Dig deep enough to be able to slip your shovel or spade under the main root mass of the rose.
Don your garden gloves and grasp the crown of the rose with both hands and use your body weight to pull the plant up and out of the soil. Excavate more deeply if the crown and main roots do not pull out easily and pull again until the mass is released from the soil.
Excavate and pull any remaining pieces of root material from the soil and smooth the soil down to level.