Others have already correctly pointed out that you'll need a (periodic) interrupt source and facility to handle such. As the Z80 doesn't provide a protected or system mode, it needs to be a non-maskable interrupt, which the Z80 fortunately does provide (iirc, that wasn't used in the Amstrad computers though).
Sure you'll need to save the registers, but you could do that using the stack as well. The second register set just makes it quicker.
