Dubinsky, who had 16 goals and 34 assists one year ago, was injured in practice on Monday.
Cracknell, a physical 6-foot-2, 210-pounder who was Calgary's ninth-round pick in the 2004 draft, had six goals and 10 assists in 65 games with the St. Louis Blues the last four seasons.
D'Amigo cleared waivers before being assigned to Springfield.
Blue Jackets coach Todd Richards said Dubinsky (lower body) and defenceman Ryan Murray (knee) are day to day and will not play in Thursday's season opener at Buffalo.
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