Aims. We present a new wide-field spectroscopic survey of the galaxy cluster SMACS J0723.3-7327 at z ∼ 0.39, with the aim of mapping the large-scale structure around this massive cluster. We also aim to detect infalling galaxy groups in combination with XMM-Newton and eROSITA X-ray data, while studying the evolution and transformation of cluster galaxies out to ∼ 2r<inf>200</inf>. Methods. We carried out new multi-slit spectroscopic observations of SMACS J0723-3-7327 with the IMACS f/2 instrument on the 6.5 m Magellan-Baade telescope, obtaining spectra for 193 galaxies selected using deep near-infrared (NIR) photometry from the Galaxy Clusters at VIRCAM (GCAV) survey. We examined the infall pattern of galaxies in the caustic diagram out to ∼ 2r<inf>200</inf> and used it to identify 93 cluster members from our sample as being located within the caustic curves. Incorporating redshifts from previous studies of the cluster core, we produced a catalogue of 150 spectroscopically-confirmed cluster members. Results. We measured a central cluster redshift of z = 0.3910 ± 0.0007 and a velocity dispersion of σ <inf>V</inf> = 1431 ± 150 km s- 1 for galaxies within r<inf>200</inf>. We found sub-structures within the velocity distribution function and a filamentary structure passing SE-NW through the cluster, likely related to the highly elongated mass distribution and X-ray emission seen in the central regions of the cluster. Using an optical colour-colour separation, we determine the fraction of star-forming galaxies as a function of cluster-centric radius out to 5r<inf>200</inf> using photometric data, finding it consistently lower compared to coeval field galaxies even at 5r<inf>200</inf>. We identified a number of clumps of red galaxies in the cluster infall regions, suggestive of infalling groups in which galaxies could be undergoing pre-processing, even if we were unable to detect any associated X-ray emission in the XMM or eROSITA data. Conclusions. This work confirms the dynamical complexity of cluster SMACS J0723.3-7327 and the surrounding large-scale structure, similar to that seen for other massive clusters at z ∼ 0.4. Further spectroscopic analyses across larger cluster-centric distances are essential to comprehensively assess the dynamical state of the cluster and investigate how environmental mechanisms influence star formation quenching in galaxies at varying radial distances. © 2025 Elsevier B.V., All rights reserved.