I don't have a clue as to your rose's identity. Detailed photos of the flowers, leaves, and thorns would help, along with its size, growth habit (shrub, climber, rampant rambler?) and any history of it that you know. I can, however, offer some deadheading advice based on what I'd do if it was my own rose.

Do you know where this rose wants to put out its new growth? If not, snap off each flower individually. I usually just do this by hand -- it's also a good way to check to see if your rose is well hydrated . . . easy to snap = well watered . . . bends and doesn't snap easily = needs water. This will leave a naked candelabra, but don't dispair. The little stems that are left usually yellow and die on their own. For some roses growth will start from within this cluster of stems, or it may begin somewhere on the main cane below the cluster. Cut off the part of the stem above the new growth, you will know how to deadhead the rose at the most optimum point in the future.

Connie

You know, that picture is mostly of the backsides of the flowers. Do you have any other pictures that show the front sides?