I hear a tone like sound in the door. The battery goes dead every two days. What could be the problem???

There is no battery in the door, you might have a faulty door switch which is acting like a parasitic drain on the battery.

What happens if I cut the cord??

I'd find the faulty door jamb switch (if that is in fact the problem) and either replace it or tape it shut or otherwise disable it. You really don't want to be cutting wires, as I'm sure you have a speaker in your car door you'd like to have working, power windows, etc. Door jamb switches are dirt cheap (around $10-15) and shouldn't be too much trouble to access. Again, i'm just guessing at what might be at fault. If you have a sound coming directly from the door (as opposed to the door open chime) then you might have a fault in the door, such as a bad or stuck window regulator or even shorted speaker. Pop the interior door panel off and try to find the source of the sound.