In this study, nanocellulose aerogels with a tunable Poisson’s ratio were fabricated. Tissue engineering scaffolds with a tunable Poisson’s ratio may be better able to simulate the mechanical behavior of natural tissues. A mixture of cellulose nanofibers (CNFs) and polyethylene glycol diacrylate (PEGDA) was used as the raw material to prepare CNF/PEGDA aerogels with a multiscale pore structure through a combination of stereolithography (SLA) and freeze-drying. The aerogels were fabricated with a regular macropore network structure and a random and homogeneous distribution of micropores. The macropore structure of the scaffolds could be customized through SLA, which resulted in scaffolds that exhibited one of three different mechanical behaviors: positive Poisson’s ratio (PPR), negative Poisson’s ratio (NPR) or zero Poisson’s ratio (ZPR). Then, the hydrogel scaffolds were transformed into aerogel scaffolds through the freeze-drying method, which endowed the scaffolds with homogeneously distributed micropores. The material ratio and exposure were adjusted to obtain scaffolds with a clear pore structure. Then, the CNF/PEGDA scaffolds with different Poisson’s ratios were subjected to mechanical tests, and their chondrogenic induction characteristics were determined. The NPR scaffold not only provided a good environment for cell growth but also affected mouse bone marrow mesenchymal stem cell (mBMSC) proliferation and chondrogenic induction. Thus, we provide a feasible scheme for the preparation of three-dimensional scaffolds with a multiscale pore structure and tunable Poisson’s ratio, which contributes to cartilage repair in tissue engineering.