A mechanic said my 2001 Chevy astro needs a 1600$ rear differential rebuild
Sounds extremely expensive to me.
Is it a reasonable cost?
Is there a way to save the car without it?

Get a second opinion.

Only use full synthetic gear lubricant in differentials; e.g. Mobil 1 Synthetic 75W-90 EP Lubricant, GL5. Then, you shouldn't ever have any problems with your differential, provided you fill it to the proper level. Change it every 100,000 miles, while the differential is at normal operating temperature.

a mechanic said my 2001 Chevy astro needs a 1600$ rear differential rebuild
sounds extremely expensive to me.
Is it a reasonable cost?
is there a way to save the car without it?

$1600 parts and labor including diagnosis? That doesn't sound too bad to me. It pays to ask questions, like is the replacement used, rebuilt, new, etc. What kind of warranty? It can also pay-off to shop around.