What's the setting like? Terrain will be a big factor.
Armies need to march and that requires a lot of food and water. Taint their supplies. You can use poison or disease to do this. If you can't get close enough to the army to infiltrate the food and water supply you can always taint the next major water supply they will encounter, be it a river or lake.
Infiltrate the army by passing along false orders from their superiors. The party could use a number of means depending upon what's available to them, such as illusions or charm person.
Organize a raid by elves, orcs or some other army to stage a hit and strike battle against the army. If they suffer enough casualties or injuries they will be slowed considerably. They will even be a weaker fighting force once they arrive at their destination. Keep in mind the more severe the injuries, the longer it takes to heal, this alone slows them down.
If the terrain is difficult such as a canyon, a landslide can cause them to reroute, thus losing valuable time.