To provide dicing pressure-sensitive adhesive sheets capable of preventing the occurrence of threadlike waste on dicing without suffering from a reduction in the quality level of a product and a disadvantage from a cost standpoint.

A dicing pressure-sensitive adhesive sheet 1 has, on a substrate film 11, a pressure-sensitive adhesive layer 12 for affixing a substance to be cut, and the substrate film has a monolayered or multilayered structure and, simultaneously, at least the layer in the substrate film which is brought into contact with the pressure-sensitive adhesive layer is constituted by a semi- compatible or non-compatible polymer blend of at least two types of polymers. At least one type of the polymers constituting the polymer blend is a high crystallinity olefin based resin having a degree of crystallinity of not less than 40% and, at the same time, the ratio of the polymer in the polymer blend can be 1 to 50 wt.%. Further, at least one type of the polymers constituting the polymer blend is a low crystallinity olefin based polymer having a degree of crystallinity of less than 40% and, at the same time, the ratio of the polymer in the polymer blend can be 50-99 wt.%.