Are these claims true?: No, there is no evidence to prove that Putin issues such an order. Furthermore, the article going viral was published on 4 March on a website called 'Real Raw News'. The website's "about us" section mentions that it contains humour, parody, and satirical content.
Ironically...: On 4 March, TASS - a Russian news agency - published a report which mentioned a press release from the Ministry of Health.
It said that batches of Sputnik V vaccines had been sent to Moscow and other regions. However, the other regions were not specified.
The press release also said that the vaccine protects against COVID-19. It mentioned, "Vaccination and timely revaccination are especially relevant for people over 60 and people with chronic diseases such as cardiovascular, diabetes and others."
No such order is available in the public domain: We checked the official website of the Kremlin but did not come across any such order that directed the destruction of COVID-19 vaccines.
Further, no credible news reports were available which talked about such an order from the Russian President.
Conclusion: A fabricated article from a website which publishes "satire, parody, and humour" content is being shared to claim that the Russian President has ordered the destruction of all COVID-19 vaccines in the country.