Hi mate
As far as I can see it punching dies should be made from tool steel. It's harder than normal mild steel and requires rigid mill. The shape of your alu plate forces to use CNC mill.
The male part of the die (egg shape) can be grind to shape but the female part have to be milled.
I'm not die expert (never did any)l, but do you think, because it is only 1mm thick aluminium, would mild steel be tough enough to work as a punching/cutting die. What about to consider carburising/case hardening after machining ????
I believe, in case of profiling/bending dies, mild steel could be sufficiently hard for this purpose.