Not unless you are under an Interest Only mortgage product.

Even if you have an adjustable rate mortgage (ARM) any additional payment to principal will reduce the total interest you pay over the life of the loan and will reduce the number of years in which it will take you to payoff your mortgage.

Certain banks allow for a large principal reduction and then they will re-amortize the remaining balance. BB&T is one of the banks that I know will do this. A lump sum payment of $10,000 will likely not be enough to make it worth it to re-amortize. The difference in payment would likely only be $50 - $75 per month depending on how seasoned the existing loan is. 

Most lenders have a recast option available. I have seen this fee range from $100 to $250.

Flagstar is another lender who allows it, I would call your lender and ask them.