Despite its grounding in creativity techniques, merging multiple source sketches to create new ideas has received scant attention in design literature. In this paper, we identify the physical operations that in merging sketch components. We also introduce cognitive operations of reuse, repurpose, refactor, and reinterpret, and explore their relevance to creative design. To examine the relationship of cognitive operations, physical techniques, and creative sketch outcomes, we conducted a qualitative user study where student designers merged existing sketches to generate either an alternative design, or an unrelated new design. We compared two digital selection techniques: freeform selection, and a stroke-cluster-based object select technique. The resulting merge sketches were subjected to crowdsourced evaluation of these sketches, and manual coding for the use of cognitive operations. Our bindings establish a firm connection between the proposed cognitive operations and the context and outcome of creative tasks. Key bindings indicate that reinterpret cognitive operations correlate strongly with creativity in merged sketches, while reuse operations correlate negatively with creativity. Furthermore, freeform selection techniques are preferred significantly by designers. We discuss the empirical contributions of understanding the use of cognitive operations during design exploration, and the practical implications for designing interfaces in digital tools that facilitate creativity in merging sketches.