Mixing SATA and SAS drives on same controller
You can mix SATA and SAS on the same controller. I do it sometimes. It works best when you have dedicated drive connections (e.g. 4-lane connectors to a non-oversubscribed backplane or to a 4-disk breakout cable).
Just avoid mixing types when a SAS expander is involved. The reasoning?
...direct attaching SATA disks to SAS HBAs should work just fine. It's when you add SAS expanders (and SATA Tunneling Protocol) to the mix that you start encountering weird errors with misbehaving SATA disks. SATA simply isn't designed with a switching fabric in mind, and it looks like firmwares still aren't robust enough to deal with command tunneling reliably in the presence of errors.