Let's look at the phrase further and address two particular points:
1. Why it is in fact correct to use "hoist" (as opposed to "hoisted").
2. Why in fact the more authentic version uses the preposition "with": to be hoist with one's own petard.
This expression comes from Shakespeare's "Hamlet", Act 3 Scene 4, lines 202 - 209:
HAMLET
There's letters seal'd, and my two schoolfellows,
Whom I will trust as I will adders fang'd—
They bear the mandate, they must sweep my way
And marshal me to knavery. Let it work;
For 'tis the sport to have the engineer
Hoist with his own petard, an't shall go hard
But I will delve one yard below their mines
And blow them at the moon.
The Oxford English Dictionary gives the expression its own entry, "hoist with his own petard", not "hoisted" or "by", though some subsidiary dictionaries at the publishers allow "by" in brackets, like so: "be hoist with (or by) one's own petard".
Hoist is/was the past participle of the now-obsolete verb hoise. Hoise simply meant "to raise with effort or exertion". A petard was a bomb. So the literal meaning is "to be launched into mid-air by his own bomb".