The gelding was euthanised at the course.
The nine-year-old was in his 18th jumps race - having had more than 100 starts on the flat - when he fell with another horse with about 800 metres to the finish.
To date this season, three horses have died in jumps racing in South Australia, with Tradesman's Choice joining Marc of Thunder and Satu San.
Two horses have died in Victoria - the only other Australian state that still allows jumps racing. They were Sirrocean Storm and Prince Vitality.
The sport has been under intense scrutiny over the toll taken on racehorses, with opponents pointing out that jumps racing is 10 to 20 times more dangerous than racing on the flat.
In Victoria, its future depends on keeping fatality and fall rates within certain limits set by racing administrators.