You can! But you don't want to use a 'sucker' that is coming from the graft, because that would become the same as the graft. You need to use a cutting from the scion, the part that flowers. The best way is to take a cane that has recently bloomed and cut it down to where it meets the next cane and get some 'heel wood'. then you can apply some rooting hormone and put the cutting in some potting soil. You have to keep it moist, but not wet. The success rate may vary. There is a lot of information on the internet about how to do cuttings.

Good advice Buford! not that you need my affirmation, lol.

What we were advised to do out here with roses that were budded on Multiflora (not a good rootstock for us) was to plant them very deep. Over a period of time they transitioned onto their own roots -- while using the "boost" from the Multiflora to give them a kick-start.

It really did work! Judging from what we saw when we dug roses up much later, the Multiflora eventually died off, once you got substantial roots from the scion. And THAT was a relief, because that Hortico/Pickering Multiflora rootstock suckered like crazy. I was really glad to see it go.

If you are just trying to make another (ownroot) rose from the 1st grafted rose, you can also pull down a cane, depending on the growth habit, and start the rooting process that way. Put a rock or something to keep part of the cane under dirt, and eventually it will root and you can cut that new plant off from your original plant.

Meredith has some good advice. It might be easier to use what they call the "layering" method to root a cane and then cut it off. You'll have a much better success rate because the mother plant will still be feeding the cane while the section that's under the soil will put out roots. I recommend what Meredith says.

Jerri has some great advice too, but you'd have to dig up the rose or build a raised area around it in order to get it deeper into the ground once its planted. If the rose is newly planted and sill easy to move (has not yet set out delicate feeder roots, within a week) you can do that. If not, try rooting it using the layering method above.