Yeast can reproduce sexually, but only if they're haploid (have a single set of chromosomes). Commercial yeast products are almost 100% diploid, or sometimes even higher polyploids. In order to get a significant amount of sexual reproduction, you'd need to force the cells to undergo meiosis, which basically means putting them under significant stress for multiple generations - very high temperatures, very high-gravity wort, etc. Obviously that wouldn't make very good beer though.
For the most part, what's going to happen when you mix two strains is that one will reproduce faster than the other, even if only slightly, and end up dominant. There was an article about it BYO a few months ago.