I know you are a little panicked and in a hurry for help...
But we need MUCH more information then what you provided.
First, please tell us how old, or more importantly how big your beardie is, how long from end of tail to head (at least a good approx length.. I understand you may not wanting to be trying to measure him/her now)
Also we need to know how big is the cut? A photo or two would be VERY helpful, here is a link to how to post photos right in your response... it's pretty easy:
http://www.beardeddragon.org/forums/viewtopic.php?f=30&t=167225
I am not experienced enough to say anything to help you besides getting your pet to a vet asap. If there are any good home remedies, I don't know what, and I doubt anyone else will either without having much more info, and remember that "a photo is worth a 1000 words" - so please try and get us a photo or two.
THIS IS STRICTLY A GUESS BUT IT MIGHT BE WHAT I MIGHT TRY IN A PINCH... If it was a minor cut and no blood or not bleeding, I MIGHT try giving the beardie a nice warm
bath and making sure the cut is covered in water, but not too deep to risk your beardie drowning obviously... just barely covered - and keep the cut below the surface of the water for as long as you can, 20 min if possible, and try and keep the water luke warm, don't let it get cold.
Again, that's just what I might try depending on the severity of the cut. Anyone here will need to know much more info then you provided to give you any good advice and until then the only sure, good advice I can give you now is "Get your pet to a vet ASAP"
Help us help you. Photos please, more info, how it happened, how deep and long is the cut, how big is your beardie, etc etc...