Yes, you have to send the corrected 1099-MISC form to the IRS and the contractor. 

Use a separate Form 1096 for each type of return you are correcting.  See General Instructions for Certain Information Returns - IRS.gov

Enter an “X” in the “CORRECTED” checkbox only when correcting a form previously filed with the IRS or furnished to the recipient. Certain errors require two returns to make the correction. See Filing corrected returns on paper forms later to determine when to mark the “CORRECTED” checkbox. See the screenshot below.