Can you cut a smoker's tongue after it wraps around you?

You can't cut the tongue with a melee weapon once you've been ensnared however you can cut the tongue while its coming at you. If you have a melee weapon, it is possible to cut the tongue just before it hits you. This tactic require timing and knowledge of the direction of the tongue. If you have a Chainsaw, timing and direction is usually not needed. If the Chainsaw is in use at the time the tongue hits, the tongue will be unable to constrict you.

When you have been ensared you can for a short period of time :

• Shoot the tongue
• Shoot the Smoker
• If you are close enough try a melee attack to push the smoker back
• Throw a pipe bomb (preferably). You can try a molotov cocktail but I'd advise against it since you'll die faster if you aim badly
• If there is a door between you and the smoker, closing it will break the tongue

You can find more information about the smoker and general mechanics on the wiki

There is an achievement in L4D 1 (it might be in L4D 2 as well) for shooting the smoker before you are fully constricted and freeing yourself. You only have a few seconds to do so but it is possible (with ranged weapons at least). I haven't tried doing it by taking out the tongue but I have killed the smoker a few times.

Once you are fully constricted you are helpless (as you say L4D is designed to encourage teamwork which is why so many special attacks incapacitate a single target) but you do have that small window to free yourself.