The viscoelastic behavior of early-age cementitious materials is particularly significant in applications such as 3D concrete printing, where time-dependent deformation can affect performance parameters such as shape retention. In this study, stress relaxation tests were carried out on fresh 3D-printable concrete mixtures. Two types of mixtures were examined: a control mixture prepared with Portland cement, and another incorporating a limestone–calcined clay addition. An amplitude sweep was first performed to identify the linear viscoelastic region (LVER), and a strain level corresponding to 40% of the LVER limit was selected to ensure linear viscoelastic response. Relaxation tests were conducted on samples with different ages—1, 10, 20, and 30 min after mixing—by applying a constant shear strain and recording stress decay over 100 s. The results revealed a substantial stress relaxation capacity, with more than 40% of the initial stress dissipating within 100 s. The LC2 mix exhibited higher stiffness development and a slower stress relaxation rate compared with the control, indicating a more elastic-dominated response at early ages. The relaxation modulus, calculated by normalizing stress over time with the applied strain, showed good agreement with the generalized Maxwell viscoelastic model having two relaxation times. These insights enhance the understanding of early-age viscoelasticity and offer valuable input for modelling buildability and evaluating time-dependent stresses arising from plastic shrinkage and thermal effects during early-ages in 3D-printed concrete.