Airy wavepackets, distinguished by their unique self-accelerating, self-healing, and nondiffracting properties, have found extensive applications in particle manipulation, biomedical imaging, and material processing. Investigations into Airy waves have predominantly concentrated on either spatial or temporal dimensions, whereas studies on spatiotemporal Airy wavepackets have garnered less attention owing to the intricate nature of their generation systems. In this study, we present the generation of spatiotemporal Airy wavepackets by employing discrete frequency modulation and geometric phase modulation of pulses from a mode-locked fiber laser. The properties of Airy wavepackets are dictated by the imparted cubic frequency phase, geometric phase, and polarization state, resulting in controllable spatiotemporal profiles. The self-healing properties of spatiotemporal Airy wavepackets have been confirmed in both temporal and spatial dimensions, demonstrating substantial potential for applications in dynamic microscopy imaging and high-speed optical data transmission.