"My birthday party is on Saturday."
Translation:Mi fiesta de cumpleaños es el sábado.
Surfing round, I don't find any good explanation -- I think it's just the idiom. Rather like we'd say "festival of song," except we'd also say "song festival" and -- looking at google results -- they just don't do a switch like that.
Prepositions are always arbitrary and weird and never translate consistently between languages. Just when you think some little word means "of" or "by" it turns out that it's used for "on" or "to" under other circumstances.
You wrote "mi de compleanos fiesta es el Sábado" which would translate directly to "my of birthday party is on Saturday". This makes no sense
The correct way of saying this would be "mi fiesta de cumpleaños es el sábado" which directly translates to "my party of birthday is on Saturday" but is understood as "my birthday party is on Saturday".
Do you see the mix up in word order here?