Adhesion at the dissimilar interface of single wall carbon nanotube (SWCNT) bundles and electrospun polymer nanofibers (Espun) was directly measured using a nano cheese cutter. A sample fiber suspended at the tip of an atomic force microscope cantilever and another freestanding fiber on a mica substrate were arranged in a cross-cylinder configuration and allowed to adhere. External tensile load led to spontaneous detachment or "pull-off'. Adhesion was shown to be dominated by van der Waals attraction, and the detachment process conforms to the classical Maugis parameter in the JKR-DMT transition.