Fructo-oligosaccharides (FOS) are one of the most well-studied and commercialized prebiotics. FOS can be obtained either by controlled hydrolysis of inulin or by sucrose transfructosylation. FOS produced from sucrose are typically classified as short-chain FOS (scFOS), of which the best known are 1-kestotriose (GF2), 1,1-kestotetraose (GF3), and 1,1,1-kestopentaose (GF4), produced by fructosyltransferases (FTases) or β-fructofuranosidases. In previous work, FOS production was studied using the Aspergillus oryzae N74 strain, its ftase gene was heterologously expressed in Komagataella phaffii (Pichia pastoris), and the enzyme’s tertiary structure modeled. More recently, residues that may be involved in protein–substrate interactions were predicted. In this study, the aim was to experimentally validate previous in silico results by independently producing recombinant wild-type A. oryzae N74 FTase and three single-point mutations in Komagataella phaffii (Pichia pastoris). The R163A mutation virtually abolished the transfructosylating activity, indicating a requirement for the positively charged arginine residue in the catalytic domain D. In contrast, transfructosylating activity was improved by introducing the mutations V242E or F254H, with V242E resulting in higher production of GF2 without affecting that of GF3. Interestingly, initial sucrose concentration, reaction temperature and the presence of metal cofactors did not affect the enhanced activity of mutant V242E. Overall, these results shed light on the mechanism of transfructosylation of the FTase from A. oryzae and expand considerations regarding the design of biotechnological processes for specific FOS production.