They differ.
как только
is a conjunction which can introduce subordinate clause of timing, translated as soon as
, right after
вот только
can't function like that, it can be translated as just
or simply
and вот
is added for emphasis but can be omitted
So this sentence in English should read something like
Just let me graduate (first), OK, and I'll leave you right away....
OR
Just wait till after I graduate, OK, ....
It can be used in contexts where it doesn't express displeasure of the speaker, in these cases it imparts the statement a tenor of promise or prediction i guess.
вот только
too can be translated as soon as
but in Russian it's not a full synonym of как только
and it only can introduce first clause in a compound sentence.
Когда школа я не болею, а вот только начнется лето, (и) я сразу же заболею
Rehashing the sentence by swapping clauses to read
Когда школа я не болею, но я сразу же заболею, вот только начнется лето
doesn't sound idiomatic, unlike it would do with the conjunction как только
In this function вот только
in one clause is often (or perhaps always) coupled with adverbs either of immediacy (сразу (же)
, тут же
, тотчас
) or surety (обязательно
, непременно
) in the next clause and requires verbs in future tense in perfective aspect in both
вот только ...., (и) сразу/тут же
/ обязательно
....
Depending on the context either part of вот только
can be omitted.