Femtosecond optical vortices open a variety of fascinating applications, ranging from femtosecond micro-nano manipulation to vortex strong-field physics. A basic requirement for these applications is that the femtosecond vortex has a clean intensity node for capturing or trapping particles. Thus far, the generation of clean femtosecond vortices remains a challenge. Here, we report on ultraclean femtosecond vortex generation by a femtosecond mode-locked laser operating in a single high-order transverse mode. By controlling the oscillation thresholds of various-order transverse modes in a laser, a pure and mode-order-tunable femtosecond Hermite-Gaussian beam is generated from the mode-locked laser and, subsequently, is converted into the femtosecond vortex by a cylindrical lens mode converter. The obtained femtosecond vortex has an unprecedented ring-to-center intensity contrast of 36 dB measured with a near wavelength-spatial-resolution detecting device, which approaches the theoretical limit of an ideal vortex beam. This Letter may open a wide range of application prospects for femtosecond vortices and motivate novel femtosecond structured beam generation directly from mode-locked lasers.