I wouldn't call this a distortion as it is a 'new', synthesized sound based on the original sound. A distortion would be the original sound, shaped (see waveshapers)
I believe this is a sine wave that is modulated based on the characteristics of the original phrase. It sounds like the pitch follows the original pitch. The envelope (the way the amplitude varies through time) follows the original envelope and there was an attempt to do the same with timbre by something that sounds like FM synthesis to my ears.
I can't give you an exact 'recipe' for this patch but I would start with a digital modular synthesizer, Reaktor or Max MSP since this kind of tools allow the flexibility to build a patch like this.
The easiest part is the envelope - use an envelope follower and route it to your final amplitude, usually a VCA.
Pitch is quite tricky and I can't tell you how to do it but in principle, you need to use FFT to analyze the incoming signal, find the highest peak in the spectrum diagram and plot how it moves against time. This curve needs to control the pitch of a sine wave oscillator.
Timbre is also tricky. If I'm getting this right, they are using the amplitude of the incoming signal (modulator) to control the amplitude of fixed frequency sine wave oscillator which in turn modulates the frequency of our first oscillator.