I had a rope bridge in my last D&D session - unfortunately I played the monsters poorly and they didn't get a chance to try to cut the bridge, but that was my intent.
Other than cutting the bridge, I didn't really have any special mechanics to it.
Basically, the bridge was made of 4 ropes, with wooden slats between the bottom two.
0 ropes cut: any model pushed off the bridge gets 2 saving throws to avoid it - make both, and they don't fall prone.
1 rope cut: lose the above special rule
2 ropes cut: all on bridge must make saving throw or fall. Persons on the bridge count count as slowed and grant combat advantage to those not on the bridge
3 ropes cut: same as 2 ropes, but no need for an additional saving throw.
4 ropes cut: all on bridge fall.
Or that's how I seem to remember it working - I seem to have thrown out my encounter page. I think the ropes were AC 10 and had 10 HP. Incidentally, the party was level 3 and a fall would have done 3d10 and essentially removed the player from the fight for as long as it took them to climb up a 30ft cliff.