Processor design: turning blocks on/off dynamically to save power?
Yes, you can power down specific sections of a chip.  In general you don't see this in CPUs by shutting down sections of hardware like the excess FP blocks (like you suggested), mainly because this would lead to weird behavioral changes in the logic based on whether or not an instruction used the powered down blocks.

Where you do see it is in two places:


Power-managed CPUs with multiple cores.  The operating system can shut down unused cores in periods of low CPU utilization, but then the operating system will decide when to activate the core, and the core will alert the operating system when it is active.  In the meantime, the operating system shunts all operations to the active core (or cores).
On microcontrollers you can activate and deactivate certain functionality by providing power to the functional section of the die.  So for example: on most chips you can power or choose not to power the analog to digital converter, and not powering it (even when not in use) will save you some small amount of power (which can be important in very low-power applications).


How you "power down" a section of a chip is pretty straightforward: you have a power transistor that controls the positive input rail to all of the transistors in a section of the chip die, and you turn that on and off.