Listen to We've Got a Groovy Thing Going online. We've Got a Groovy Thing Going is an English language song and is sung by Karaoke Diamonds. We've Got a Groovy Thing Going, from the album Simon & Garfunkel - The Best Songs (Karaoke Version In the Style of Simon & Garfunkel), was released in the year 2011. The duration of the song is 1:51. Download English songs online from JioSaavn.