Thermoresponsive shape memory polymers (SMPs) are a promising research area with significant potential in smart grippers, wearable electronics, and biomedical devices. The present study introduces a thermoresponsive SMP consisting of a maleic anhydride grafted polystyrene-block-polyethylenebutylene-block-polystyrene-triblock copolymer (MA-g-SEBS) and plant-derived nanofibrillar cellulose (NC). In contrast to most of the studies that utilize hydrophilic nanoscaled cellulose, this study employs surface acylated nanofibrillar cellulose (a x NC). The acylation process facilitates enhanced interaction between a x NCs and the polymer matrix, improving tensile strength, elongation at break, and storage modulus for dynamic applications. Furthermore, it aids in aligning the copolymer chains parallel to the cellulose fibrils. The orientated composite exhibits a high shape recovery percentage of approximately 92% when subjected to torsional strain owing to stored elastic energy. The acyl groups grafted onto the NC surface have the ability to create an additional domain within the MA-g-SEBS matrix, resulting in an excellent shape fixity (∼94%). Additionally, the cytocompatibility and cell adhesion studies indicated favorable biocompatibility of the composite. This work presents an efficient, eco-friendly approach for developing a sustainable cellulose-based multifunctional shape memory composite suitable for biomedical applications.