Can bagworms kill trees

Yes, bagworms should be killed since this larval stage of case moths (Psychidae family) can defoliate trees and the chrysalis and the moth stages can cut off internal arboreal fluid circulations with the delicate-looking, super-strong thread by which pupae and adults hang from twigs. It is an unfortunate case of the adult living just long enough to mate and not cause trouble other than leaving behind many eggs that will turn into voracious caterpillars.

Any stage in the lepidopteran in question's life cycle may be controlled by manual or mechanical removal while natural enemies include entomopathogenic bacteria and nematodes, ichneumonid parasitoid wasps, parasitic wasps, sparrows and white-footed mice and treatments focus upon the egg and larval stages before mid-summer.