It depends on type of the garden. Most likely no one will kick you off, but in general try to avoid doing so.
I live in Czechia since I was born and thats quite some time. I originate from small village (where it is not such a big deal), but currently I'm living in Brno for few years (second largest city in Czechia, after Prague). Naturally, I've visited Prague many times in my life and finally -- I consider my self huge beer lover, so I think I've got some insight into this topic.
To be honest -- Czech people are very sceptic to everything they are not used to (actually everything in general) and I would avoid bringing own food to beer garden. Most likely no one will say a word (unless its explicitly forbidden, you would see the sign at the entrace), but some people will definitely judge you. It depends on you, if you are okay with that.
It is very common (almost standard), that gardens in Prague offers some 'snack' to beer, e.g. pickled sausage, crisps etc. even though it is not restaurant and it would definitely not be polite to bring your own food -- especially if garden is part of the restaurant.
Even though it is not part of the question -- I would like to mention that on the other hand, it is common bringing your own food to cinema in Czech Republic.