The suspected thief also suffered a cardiac arrest in the altercation in The Shires car park in Trowbridge, Wiltshire, on Thursday afternoon.
He was treated by paramedics but died at the scene, police said.
The 20-year-old security guard, from Trowbridge, was arrested shortly after.
He was later released on unconditional bail.
Det Ch Insp Jeremy Carter said: "He tackled the suspected shoplifter causing a number of glass bottles he was concealing to smash.
"He suffered significant bleeding from which he died."
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He said the victim, who was aged 30 and thought to be from Cornwall, was suspected of committing a number of shoplifting offences in the town and there had been "various episodes involving this individual and security staff from surrounding stores during the day".
"We need to understand whether or not the force being used was proportionate to the circumstances that unravelled during the course of the day," added Mr Carter.
"Formal identification is yet to be carried out and a post-mortem is due to be carried out later today [Friday]."
An Asda spokesman told BBC News its security staff were not involved.
A security guard was arrested on suspicion of manslaughter after an alleged shoplifter was tackled to the ground and bled to death when bottles he was carrying smashed.