No, the Destroyer has no direct mythological connection or mythological corresponding agent in the Norse legends. The Destroyer and the eventual return of the Celestials may have been considered a type of Ragnarök, the Twilight of the Gods and may be considered an allegory for that event.
The Destroyer was created as a threat capable of being a challenge to Thor in its early appearances. The Destroyer first appears in Journey into Mystery #118 (Jul. 1965) and was created by Stan Lee and Jack Kirby.
Since it could be inhabited and controlled by a spiritual/magical being, it made the perfect weapon for Loki to get an opportunity to get the physical upper hand on Thor. Loki has taken control of the weapon more than once and has nearly beaten Thor to death on more than one occasion. It would be nearly fifteen years later before a story would be created which would give the Destroyer a real reason for existing.
The Gathering of the Celestial Host in Thor #301
In Thor #301 we learn the Destroyer was an object created by all of the Earth-616 Skyfathers as a Final Solution in case of the eventual return of the Celestials, cosmic beings at least partially responsible for mutation in the human genome of the Marvel Universe. The Celestials would be coming back to Earth to judge it and if found unworthy, they would destroy the Earth.
See: What was the ultimate origin of Asgardians?
Odin, leading the Skyfathers, would absorb the souls of all the Asgardians (except Thor) inhabit the Destroyer and armed with the Oversword of Asgard, the deities of Earth would confront and challenge the Celestials. Despite its amazing capabilities against any and all forces on Earth and Asgard, the Destroyer performs poorly and is destroyed almost effortlessly by the Celestials.
The destruction of the Destroyer by the Celestials