First, it's two sentences, although periods are omitted.
Kyoto people don't say "Die!" (to someone). (Instead,) They say "Oh this person is dead" after killing them.
I think you can get the main part of this joke from the translation. Basically this is an ethnic joke that is making fun of the cold and sarcastic trait of Kyoto people. 死んではる is a Kyoto-ben version of 死んでいらっしゃる. (This tweet also shows the stereotyped image of Kyoto people. Well, who said sarcasm doesn't exist in Japan?)
In addition, 死ねどす by itself sounds funny. This どす (or どすえ, ですえ) is a stereotyped feminine (or "geisha-ish") Kyoto-ben variant of です. Naturally, it comes after a noun or an adjective, but not after an imperative form. A "correct" Kyoto-ben sentence for "Die!" would be something like 死んどくれやす. Therefore, this tweet initially looks like a serious Kyoto-ben lesson, but it turns out to be a dirty joke in the second sentence, which makes the tweet even funnier.