You cannot sell a portion of a property that has a lien against it unless the lender holding the lien releases the lien on that portion. It is highly unlikely that would even happen. Practically speaking, your most likely means of selling the acre in question would be to do a survey and split the property into 2 parcels (recording with the county), then refinance your existing mortgage onto just the new parcel with your home (if value is sufficient), leaving the smaller parcel free and clear. At that point you could sell it. Whether the benefit outweighs the cost and effort, however, is a question only you can answer.
Ted’s answer is correct, and I have used that method in the past to help clients. The only other way possible to accomplish this without a refinance would be to contact your current servicer/lender about obtaining a “lien release” on the extra acre you have in mind. They will want you to document the value of the remaining land with an appraisal, and if it is sufficient based on the risk you represent, they “may” agree to release the other portion of land you are wanting to sell. If your current rate is higher than market, then a refi is definitely the way to go. If not, then explore this method. One important note, just by subdividing, you have not changed the existing lenders lien just because you have changed the legal description. Their lien predates your subdivision, and it covers the entire parcel. Good Luck!
As mentioned above, you actually have two routes: (1) Lien Release or (2) Refinance. Both will require an appraisal. The refinance could save you money if the interest rate will be more than ½ a percentage point lower; but you will have closing costs.
The land split must meet zoning ordinances. This will include the house being within the setback requirements when situated on the new lot. You will also need to make sure that both sites have road access. This will require a surveyor. He will need to, as least, create two new legal descriptions but more likely a survey which will cost as well.
Make sure that you weigh the costs and the benefits to make sure that it will turn out well in the end. This should include the impact to the value of your residence as well.