I have never seen it happen on our type of roses we grow BUT our Dogwood bushes weep/seep after being pruned and it doesn't hurt them a bit...

Weeping when pruned is a sign that the plant was not dormant when pruned, i.e. it's juices were flowing. There are those that advocate pruning to be done when a plant is dormant (talking about plants that go into dormancy) and those that advocate that pruning is better done when a plant starts to wake from dormancy since the juice flowing helps with faster wound healing. I've seen nothing to suggest that in roses one is a particularly better practice than the other.
Nik

Some plants, such as birch trees, grapevines, can 'bleed' profusely when pruned because the sap is rising under considerable internal capillary pressure. I would imagine that, as Nik says, this is sap, rising up through the vascular system....but should not be problematic for your roses.

I always prune when the roses just start to wake up and I've never seen this happen before. Could be due to the unusual winter everyone's had. I'll have to pay close attention when I prune and see if I notice this. But, sadly, that won't be for a while yet.

I've seen sap flowing from roses after pruning more than once. The plant should be fully awake and the cane thick and green in order for this 'weeping' to be very noticeable. As Camps mentioned this is very noticeable in grapevines if pruned when they have come out of dormancy and it can take days for the sap to stop flowing.
Nik