Nope, as you spotted, this is for mini-sas which is used on some server boards and raid cards.
Sata is single point to point connections. 1 port = 1 drive. There's a couple of VERY, VERY, VERY minor exceptions to this rule (google port multiplier) but you generally need matching sets of drives that will be raided together and a controller that knows how to handle a port multiplier on one of it's ports. It's also remotely possible to get hardware port multipliers that don't require the controller to know about it, this MIGHT be an option for you.
I suspect you have a mainboard where you have run out of sata ports? Easier options than the above are a PCIe sata card or sata to USB enclosures.