Midfielder Mutch has missed the last two games with a foot injury and won't return until Saturday's trip to Ipswich.
The 20-year-old returned to training recently and just fell short of appearing in last weekend's win over Blackpool.
Winger Smith was withdrawn after 25 minutes in that fixture with a muscle problem and is a major doubt.
The former QPR man felt tightness in both his groin and hamstring and was replaced by striker Joe Mason.
Mason may deputise again but Don Cowie and Bo-Kyung Kim offer further wide options for the Bluebirds manager.
Cardiff, who are joint top of the npower Championship, have won four of their last five outings and are unbeaten at home this season.
Lee Clark will check on a couple of players nursing minor bumps and bruises for Birmingham.
None are expected to be serious and Blues could well have an unchanged squad, with Clark very much tempted to keep faith with the same starting XI who bounced back to the humiliation at home to Barnsley to secure Saturday's 1-0 triumph at Brighton.
Defenders Stephen Carr (knee), Paul Caddis (shoulder), David Murphy (hamstring) and Pablo Ibanez (broken toe) all remain sidelined.
Blues could come up against former midfielder Jordon Mutch, who joined the Bluebirds over the summer and is battling back to full fitness again following a recent spell on the sidelines.
Following their win at leaders Brighton, Birmingham would cap an impressive four days with a positive result at second-placed Cardiff, who blew away Blackpool 3-0 at the weekend.