A wrapping apparatus for wrapping a sheet of a covering material from a roll onto an outer surface of a surgical site. The wrapping apparatus includes a handle and a body portion having a housing, a first end, and a second end. The housing and the first and second ends generally defining an interior region that is configured to receive the placement of the roll. The wrapping apparatus further includes first and second spindles that are configured to allow rotation of the roll relative to the handle for the dispensing of the sheet of covering material from the roll. The wrapping apparatus may also include a cap that is operably connected to the second end, and which secures the roll to the wrapping apparatus. Additionally, the wrapping apparatus may include a cutting apparatus that cuts or tears dispensed covering material away from the roll of covering material.