Need help reading mosfet Safe Operating Area graph
The safe operating area is voltage versus current, whose product is power dissipation. The reason that the maximum current is low for, around 0.2A, versus 10V for continuous DC operation is that you have to look at the product of these values: 2W. Note that for a lower voltage drop, the device can handle a lot more current. Somewhere in the range of 0.1 and 0.2V across the channel of the device, it can handle 10A.

This 10A is the absolute limit for continuous operation: it is the highest amperage reached by the strictest dotted line (the DC line). Anything higher than 10A is outside of the DC safe area, achievable only by the time-limited safe areas. For 10 ms the device can go above 20A, but the voltage must be neither too high nor too low: it must be high enough that \$R_{\text DS(on)}\$ doesn't limit the current.