An apparatus and method for cutting continuous webs having varying thicknesses, widths, and compositions into sheets. The apparatus includes a pair of oppositely rotating web feed assemblies employing a unique floating nip and clamping mechanism which engages the web and advances it a specified length past a poised cutting blade assembly and onto a simultaneously driven exit assembly. After the desired length of web has been fed, the drive mechanisms stop, and the cutting blade assembly cycles to clamp the web on the upstream side and cut. During the cutting stroke the web is held taut on the downstream side by the web feed assemblies. Upon completion of the clamping and cutting stroke, the cutting blade assembly returns and stops at its poised position.