Can you make an electric gamma ray emmiter by adding up frequencies with freq. mixers up until you reach gamma ray herz quantities?
No you can't.

Mixers made of transistors (I'm assuming you limit the question to those so not optical mixers for example) have a limited range of operation. My guess is that the "fastest" transistor based mixers we can make today can operate up to frequencies which are less than 1 Tera Hz (\$1* 10^{12}\$ Hz).

Try to go above that 1 THz and the mixer simply does not work. Transistors simply aren't that fast.

Gamma rays are at about 100 Exa Hz (\$1* 10^{18}\$ Hz), (see EM spectrum) that's about one million times times higher in frequency.

To get a mixer to produce the higher frequency signal, it has to be able to operate at that frequency. Transistor based mixers simply can't.