Could you post photos? It may have been done intentionally - clems are often planted with roses as a support. Even if not, it would be helpful to see just how closely these are co-mingled as it will have a bearing on how easy - or not - they may be to separate.

The one photo is what they currently look like the other two are from a few years back.

Lisa's Ideas · More Info

Lisa's Ideas · More Info

Hard to tell from the 'befores' or unpruned photos but the clematis showing in the trimmed back photo is C. terniflora, aka Sweet Autumn clematis. And it is a bear of a vine and can easily smother most other roses growing nearby!! It is also considered an invasive species in some areas, so that may influence your decision.

I would not necessarily hold out hope of saving both plants by digging one or the other out. They are close enough that the roots would have completely intermingled. And based on how rampant the topgrowth of the SAC can be, I'd put good money on its root system being the dominant factor.