GTCAO is the instrument that implements Adaptive Optics on GTC. For atmospheric turbulence correction, GTCAO uses a deformable mirror. Unlike other AO systems, GTCAO does not include a dedicated mirror for low-frequency tip-tilt (TT) correction. In the absence of dedicated correction, the TT components of atmospheric turbulence are corrected by the deformable mirror (DM), using a significant portion of its working range and potentially leading to saturation. To mitigate this effect, GTCAO calculates low-frequency TT and offloads its correction to the telescope secondary mirror (M2) and primary axes. These actions optimize the use of the deformable mirror range for higher frequencies correction and extends the deformable mirror lifespan. This paper describes the approach implemented for calculating low-frequency TT from the information provided by the Shack-Hartmann wavefront sensor and the state of the DM, in both open-loop and closed-loop operation modes. Laboratory tests and telescope real observation results are also presented.