Mr Lycett, 34, had pledged to donate the cash to LGBTQ+ charities if the former England international pulled out of his rumoured £10million deal with Qatar. If he did not, he said he would shred the money.
Homosexuality remains illegal in Qatar and is punishable by up to seven years in prison.
The comic has now posted footage on social media of him shredding £10,000 after Mr Beckham remained a brand ambassador for the tournament.
In the video, the Birmingham-born comedian places huge piles of cash into a shredder while dressed in a rainbow-layered tulle outfit. It is not clear if the banknotes were real.
In a previous video, the comedian told the footballer: “If you end your relationship with Qatar, I will donate ten grand of my own money (that’s a grand for every million you’re reportedly getting) to charities that support queer people in football.
“However, if you do not I will throw the money into a shredder at midday next Sunday, just before the opening ceremony of the World Cup and stream it right here.
“Not just the money, but also your status as gay icon will be shredded.”
Beckham is yet to publicly acknowledge or respond to the comic.
The stunt sparked a mixed response from fans. One wrote: “For the people missing the point. It’s Joe’s money. If he’d have bought a watch or a car we wouldn’t have cared.
“The point isn’t about him shredding money, it’s about highlighting the issues with celebrities taking far greater sums from a country with an awful human rights record”.
However, others criticised the star for shredding vast sums of cash during a cost of living crisis.
Former culture secretary Nadine Dorries took to Twitter just hours before the stunt to urge the star to rethink.
Ms Dorries wrote: “Shredding £10k will earn Joe Lycett far more than it will cost him and is in effect a paid-for publicity stunt which has worked.
“Job done. No-one will think any worse of him now if he changes his mind at the last minute and donates it to a homeless shelter in time for Christmas.”
Another Twitter user wrote: “While I admire the point you’re trying to make, I do hope you didn’t really shred ten grand because it could’ve been used to feed so many people in need or heat their homes.”