Spent reloaded cases, or spent factory load cases?
If the latter, the Gunsmith forum might have been a better place to post.
Anyhow, the Savage 340 uses a single hook extractor made out of a bent piece of flat steel spring stock.
It could be bent, or worn out, or MIA?
Or, your chamber could be rusty or dirty.
Have you tried cleaning it real good with a bronze .30 cal bore brush & powder solvent?
If not, get the .30 cal bore brush, a short section of cleaning rod, and a cordless drill.
And have your way with it!
rc