To spawn the Furious Honey Elemental, hit any of the globs of tainted honey. All the globs will make their way to the upper level of this cave, and eventually coalesce into the named.
Every 10% of his health, the game will emote 'You have knocked loose a glob of honey.' The glob of honey will spawn near but not right next to the Furious Honey Elemental and start moving slowly towards it. It isn't a monster - it doesn't attack - but it does have a health bar and must be burned down like an add. If it gets too close it will merge with the Elemental, restoring 10% of its health.
If the glob of honey is getting too close to the Furious Honey Elemental, or if it just spawns very close to it, pull the Furious Honey Elemental away from the glob, then position yourself between the glob and the Elemental. This should give most if not all classes adequate time to burn the glob down, but if it doesn't, drag the Elemental further away again.