Answer: Based on your description I am not certain what is happening. Leaf cutter bees will sometimes tunnel into a rose cane as may borers, but you would see frass (sawdust) and tunneling at the break rather than sharp cuts.
It might possibly be rose curculio damage, although doubtful as if they are present you would also see big holes eaten in the foliage.
Deer will certainly bite off rose buds -- neatly tipping your rose bush -- but usually the deer eat them up rather than discard bits on the ground. I have heard stories of chipmunks and squirrels breaking off branch tips, perhaps with a little detective work you might see the culprit in action.
I wonder if perhaps there is a mischievous child in the neighborhood who is plucking them off? (I mention this because my own child once did this much to my surprise.)
If none of these seem plausible, you might contact your local county extension and also your retailer and see if they are aware of any unusual problems with roses in your area this month. I'm sorry I can't be more specific for you.
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