I have only one month till June, so I have decided to leave starting from now.
The sentence is still not clear. It does not explain why you've decided to leave one month before June.I have only one month till June, so I've decided to leave now.
We don't always say sentences that would otherwise be understood by other people who do not know the situation/context. Virtually every sentence that we say in casual conversations is somehow connected to the situation. Whether you know it or not -- the sentence, per se, still makes sense.
Actually, It is the first clause we should be dealing with. One can have a month until a deadline not until the month "X". Time is relative, but not that much. If you have a month 'till a certain month, then everybody has a month. So, it is better to say that there is only one month left before you do X, or is best to say "until the beginning of the next month". Some examples are below to clarify what I've been trying to say;
I have only one month until the date on the eviction warrant. (So, I'd better get packed)
I should not be here on (that) exact date, so I've decided to leave as soon as possible.
I shouldn't be here on 1st of June, so I...
My landlord reminded me that I had only one month to evacuate my apartment.
Or if you insist on having a month maybe you can use it this way. Let's say that your visa expires on 1st of June, then something like that can be said;
Ok, it's the 1st of May, my visa expires on 1st of June, so then that makes only a month. Now that all I have is a month, I should be leave as soon as I pack my bags.
But, you may have days to calculate 'till a certain month.