He is now sixth overall, 1:44 minutes behind Froome, who claimed a third-place finish on the stage.
Overall, Froome leads Aru by 18 seconds and Bardet by 51.
Porte's crash was the most dramatic as he clipped the grass verge on the inside of a bend on the lightning quick descent down the fearsome Mont du Chat, less than 25km from the finish.
Martin remounted but was involved in another crash shortly afterwards, while Porte, widely regarded as the biggest threat to Froome's title defence, received treatment for nearly half an hour at the roadside before being taken away in an ambulance.
Porte was taken to hospital in a neck brace after suffering concussion and multiple cuts.
The Col de la Biche was the first of three hors categorie climbs to be tackled on a brutal day of racing through the Jura mountains.
"I had a mechanical problem with my gears, I had to change bike", Froome said.
Porte, seen as one of the main rivals to his Sky team-mate Chris Froome, was taken to hospital, his tour over at the end of the first week.
Bardet, riding on familiar roads - his AG2R-La Mondiale team is based here - attacked on the final descent and got clear.
The 31-year-old had come into the Tour after his bid to win the Giro d'Italia in May ended in a crash - caused by a police motorbike -during stage nine to Blockhaus.
Poland's Rafal Majka (Bora-Hansgrohe) also crashed in the same incident that ended Thomas' race - and while Majka managed to ride on, he finished more than 36 minutes down to see his hopes of a high finish in Paris evaporate.
He careered across the road and clattered into Ireland's Dan Martin, bringing the two crashing.
After a well-earned rest day, the Tour resumes on Tuesday with a largely flat 178km Stage 10 from Perigueux to Bergerac, which should reopen the doors to the sprinters.