Direct Ink Writing (DIW) is an advanced additive manufacturing 3D-printing technique with significant potential for producing hydrogels in biomedical and engineering applications. This study presents a comprehensive rheological analysis of the yielding and recovery properties critical for ensuring the printability of carboxymethyl cellulose (CMC)-based hydrogels incorporating atenolol, an antihypertensive agent, as the active ingredient. The viscoelastic properties under shear conditions were examined using Large Amplitude Oscillatory Shear (LAOS) testing. To obtain both qualitative and quantitative insight into hydrogel dynamics, Lissajous-Bowditch plots and Fourier Transform (FT) coefficients were analyzed. The evaluation of stress signal anharmonicity and the decomposition of stress into its elastic and viscous components allowed for distinguishing structural evolution under flow among the tested hydrogels. Additionally, the analysis of the Sequence of Physical Processes (SPP) during each deformation cycle provided deeper insight into oscillatory yielding behavior, emphasizing the role of elastic strains in determining printability. Overall, the study offers valuable understanding of the nonlinear viscoelastic behavior of CMC-based hydrogels, providing a framework for optimizing hydrogel formulations in DIW applications.