An electrosurgical instrument has a handle and a body which position and close a jaw about a tissue site for simultaneously cutting and sealing relatively large tissue structures. The jaw includes an electrosurgical cutting member, which may be a blade or wire, against which tissue is biased along a cut line, and a clamping assembly that clamps a region adjacent to or surrounding the cut line. The clamping assembly includes sealing electrodes for heating the region and welding tissue along the side of the cut as the cutter parts the tissue. The clamping assembly preferably has first and second clamping jaws extending in parallel to grip the tissue as tension is released by the cut, allowing dependable and complete sealing of the cut ends over an extended time while the tissue is immobilized. Sealing electrodes formed of thermally conductive material may be covered by a thinner coating or thermally non-impeding or heat transfer cover, which preferably includes a material to assure biocompatibility and prevent sticking. The handle, body and jaw may be configured in the shape of a hemostat to allow simple positioning, or may be configured with an elongated body and a mechanism that operates the jaw through a stationary or telescoping handle for endosurgical use through a small incision. The blade may extend entirely to the tip, or the clamp assembly may extend forward of the blade. An energy ratio input element may attach to an energy source to apportion electrosurgical energy between the cutting member and the sealing electrodes. The element may include a pair of transformers, or a transformer with a split secondary or a tapped secondary winding, with the primary configured for connection to the output of an RF scalpel drive console. The windings of the transformer match impedances and power requirements of the different cutting and sealing electrodes to coordinate effective tissue sealing and welding with the cutting operation.