An adhesive sheet for dicing comprising a base film provided at least one surface thereof with an adhesive layer, wherein the base film comprises an olefinic thermoplastic elastomer comprising propylene and ethylene and/or .alpha.-olefin including 4 to 8 carbon atoms as polymerization components, and the peak melting temperature of the olefinic thermoplastic elastomer is 120.degree. C. or more, is free of economical disadvantages with less reduction in the quality level of products and less generation of fibrous off-cuts during dicing. In particular, fibrous off-cuts occur less during dicing when the base film contains a crystal-nucleating agent. Further, generation of chippings during dicing can be prevented by incorporation of an ethylene series polymer into the base film.