Roses are grafted because propagation is faster and easier than self-rooting. Where are you located? I grew a lot of roses from cuttings when I lived in Zone 8, California. This method will work if you live in a similar climate.
The best time is in the fall to root during the cool months of winter. Take cuttings from your prunings - select stems that have bloomed. Cut off the dried flower heads and rosehips down to the first set of healthy leaves. That is the top of your cutting. Make another cut about 6 inches down - you should have two sets of leaves. Pull the bottom set of leaves off, stick the cutting in the ground where you want your rose to grow and put a canning jar on its head. They will root by spring. Make sure to keep the ground damp under the jar.
Roses are grafted because its faster and easier than self-rooting.
Good luck!