Laser printing with cell spheroids can become a promising approach in tissue engineering and regenerative medicine. However, the use of standard laser bioprinters for this purpose is not optimal as they are optimized for transferring smaller objects, such as cells and microorganisms. The use of standard laser systems and protocols for the transfer of cell spheroids leads either to their destruction or to a significant deterioration in the quality of bioprinting. The possibilities of cell spheroids printing by laser-induced forward transfer in a gentle mode, which ensures good cell survival ~80% without damage and burns, were demonstrated. The proposed method showed a high spatial resolution of laser printing of cell spheroid geometric structures at the level of 62 ± 33 µm, which is significantly less than the size of the cell spheroid itself. The experiments were performed on a laboratory laser bioprinter with a sterile zone, which was supplemented with a new optical part based on the Pi-Shaper element, which allows for forming laser spots with different non-Gaussian intensity distributions. It is shown that laser spots with an intensity distribution profile of the “Two rings” type (close to Π-shaped) and a size comparable to a spheroid are optimal. To select the operating parameters of laser exposure, spheroid phantoms made of a photocurable resin and spheroids made from human umbilical cord mesenchymal stromal cells were used.