Almost everyone in the city got robbed at least once while in their cars, but it's still safer than walking or biking. I got robbed once, in over 16 years I lived in the city. They stole just some bucks I had laying around and a cellphone.
You see a lot of people that share rides, but you have to live almost in the same street and work at almost the same place so it makes sense.
You could bike, but keep in mind that the city is very rainy, so it's not a solution for everyday. There are not many bike lanes in the city, and the few that exist are not on the most busy roads, so you actually have to bike way longer than 10 miles in that example. I would not bike in São Paulo on a day to day basis for that distance.
But robbers don't usually take cars, they rather go for wallets, watches and cellphones instead.
kidnaps are very common as well. São Paulo has what they call lightning kidnaps. The robber enters your car and makes you drive around the city cashing money out of ATMs and then they just leave. The banks have adapted to that, and if you take money from 2 different ATMs in a short spam the card will get blocked for a day or two. I was never kidnaped but I know at least 4 people who had.