Question: > 
> Two long sharp teeth
> 
> 
> Two holes beneath
> 
> 
> My bite is neat
> 
> 
> I do not eat
> 
> 
> 

What am I?

Answer: 
Well this is far fetched, but let's try:  

It is

> 
>  scissors 
> 
> 
> 

Two long sharp teeth

> 
>  Scissor has two blades 
> 
> 
> 

Two holes beneath

> 
>  you can make two holes with their blades, or as @Shahriar Mahmud Sajid mentioned in comments, it can refer to the two holes used to hold the scissors.
> 
> 
> 

My bite is neat

> 
>  When they cut something, they cut neat
> 
> 
> 

I do not eat

> 
>  they don't eat :)
> 
> 
>
Let's give this a try:

> 
>  a paper punch
>    
> 
>   
> 
>  Leaves two neat holes in paper with long metal rods and doesn't require to eat.
> 
> 
>