Implementing/using a SATA controller
A number of ARM SOC chips have provision for a SATA interface, so I don't think that requirement is a particularly huge barrier. For example, the Allwinner and Texas Instruments ARM-based SOCs- SATA and even SATA II are available. 

Simply make sure that you're using a chip that supports SATA and feed it copious amounts of memory, a real operating system such as Linux, and a lot of cycles to make it happen. If the requirement is written in from the start, I don't think it will be your biggest problem. It does push the required level of hardware sophistication up to around the Raspberry Pi level (GHz-class CPU with lots of memory).