Due to its nature of dealing critical hits when under the effect of a movement-speed buff, the Affix "Increases your movement speed after the death of an enemy for 5 seconds" synergises quite well with Swift Sword, as it will require the death of a single enemy to substantially increase its effectiveness.
The mutation Frenzy works well in tandem with the Swift Sword as both the critical and health leech will be active upon acquiring a movement-speed buff, enabling one to heal a significant amount of health while also dealing critical hits.
The Velocity mutation makes the critical hit time window three times as long.
Note, however, that this mutation only increases the duration of the standard multi-kill speed boost; it does not affect other speed boost effects, such as from weapon affixes.
The Masochist mutation grants a movement speed increase upon receiving trap damage, and caps the trap damage at 10% of the player's max HP. This is highly effective against bosses such as the Giant and the Hand of the King, which have traps within their arenas.