I have a sprite at a battlefield, i have a ravenbloom student at base. my opponent play elder dragon and target the spirte at battlefield and ravenbloom student at base. i play hidden card smoke and mirror to swap the sprite and ravenbloom student location. since everything resolve backwards. the sprite and ravenbloom student will swap location first. then the elder dragon ability will try to target a sprite at battlefield and ravenbloom student at base. since there is no longer a sprite at battlefield and no longer a ravenbloom student at base. the ability will not hit any valid target and both unit will survive. Is this interpretation correct?

Yes — your interpretation is correct, with one prerequisite: Smoke and Mirrors only actually swaps the units if at least one of them has Temporary. A Temporary Sprite token satisfies that; a plain non-Temporary sprite would mean nothing moves (you'd just draw 1) and both units would still be where Elder Dragon targeted them.

The reasoning is right. Elder Dragon's play trigger chooses one unit at each location, and each of those choices re-checks its location restriction as the ability resolves. Once Smoke and Mirrors resolves (hidden gives it Reaction, so you can play it in response to the trigger; Rule 811.6), the Sprite is at Base and the Student is at a battlefield — neither is at the location it was chosen from, so both choices mistarget and the instruction doesn't execute (Rule 359.3.e.7). Nothing is dealt, so Elder Dragon's "any amount of your damage is lethal" passive never comes up.

This is the exact pattern the official clarification gives for Elder Dragon plus Flash: units moved to a location other than where they were targeted are unaffected. One small note in your favor: the Smoke and Mirrors still counts as a spell played, so Ravenbloom Student gets +1 Might this turn even after the swap (FAQ #12418).