The title is in reference to the mandrake plant, but is also the name of a pre-Purple band that Blackmore was trying to form in Germany when he got the call from Deep Purple's original management.
The lyrics weren't added until after rehearsals took place before the album-recording of Shades of Deep Purple in May, 1968, the group having decided that they did not want more than one instrumental track on the album.
[3] The song was conceived as a drum solo for Carlo Little (Rolling Stones' original drummer), who like Blackmore had played with The Savages, the backing band for Screaming Lord Sutch.
Bill Parkinson was lead guitarist with the Savages Jul-Sep 1966, while Blackmore had played with Sutch May-Oct 1962, Feb-May 1965 and Dec 1966 – Apr 1967, so their paths had clearly crossed.
As this song, along with "Hush," pushed the fledgeling band sky high, it wasn't surprising that word about it got back to Parkinson.
In the version of "Space Truckin'" recorded for the 1972 live Made in Japan album, riffs from "Mandrake Root" can be plainly heard during the instrumental parts.