Hydrolyzes sucrose and sucrose-6P, but fails to hydrolyze any of the phosphorylated isomers of sucrose and other phospho-D-glucosides, including maltose-6'P and trehalose-6P. Hydrolysis of terminal non-reducing beta-D-fructofuranoside residues in beta-D-fructofuranosides. Glycan biosynthesis; sucrose metabolism. Belongs to the glycosyl hydrolase 32 family.