AppDB says this:
"There is a bug in pulseaudio that crashes the DOTA2 beta. This is NOT a wine bug. Pulseaudio apparently wants exclusive access to the audio hardware and this causes a conflict that results in the crash. To resolve it, you will need two sound cards; get a second set of speakers, set the audio output to the second sound card and you are good to go."
On the page http://appdb.winehq.org/objectManager.php?sClass=version&iId=24458 there is a lot of fixes but it might be (?) Linux only and I'm not comfortable modifying my computer that much.