Stewards also gave the Finn two penalty points for the incident during the day's second session.
"When (Bottas) pulled away from his designated pit stop position, he lost control of the car when he turned into the fast lane," the stewards' report said. "He oversteered, spun and came to a stop across the fast lane near the McLaren pits.
"During the hearing (Bottas) stated that in the past they have been losing time in the pit departure. So they tried something new, which was to leave in second gear. As a result, the wheel spin was much higher and the result unexpected."
The stewards said the incident had to be considered potentially dangerous driving, given the presence of personnel in the pit lane.
Bottas has failed to finish on the podium in the last three races and is fifth overall in the championship, having scored half the points of seven-times world champion team mate Lewis Hamilton.
The Finn's contract is up at the end of the season. He had said earlier he would be surprised to get a penalty for a "normal mistake."
The drop is a blow for Mercedes as they fight a tight battle with Red Bull, who are 37 points clear in the constructors' standings afters even races.
Red Bull's Max Verstappen is 12 points clear of Hamilton. Verstappen was fastest in practice at Red Bull's home Austrian track on Friday.
The 23-year-old Dutchman led both sessions, setting a best lap of 1 minute 5.910 seconds in the morning and then 1:05.412 in the afternoon.
McLaren's Daniel Ricciardo was second fastest in the afternoon and Alpine's Esteban Ocon third.
Hamilton ended up fourth. The Briton had driven faster than Verstappen in the second stint, but his lap time was deleted for exceeding the track limits at the last corner when he went wide.
Bottas, fourth and 12th, was summoned to stewards after losing rear grip and skidding sideways as he left the Mercedes pits, coming to a halt blocking the pit lane but narrowly missing the wall.
Frenchman Pierre Gasly had been second for AlphaTauri in the first session but sat out the afternoon due to power unit problems.
Sunday's (June 27) race will be the first of two at Spielberg's scenic Red Bull Ring.
Red Bull are chasing their fourth successive victory after winning in Monaco, Azerbaijan and France. The team last won four in a row in 2013, before the V6 turbo hybrid era ushered in seven years of Mercedes domination from 2014.
Ferrari's Carlos Sainz was one of several spinners in the morning.