Epsom salt does kill slugs but not as good as regular table salt.
The regular table salt applied to the slugs body dehydrates the slug much faster and kills the slug faster as well.
You can also use some Epsom salt around areas that slugs hang out and the Epsom salt will deter the slugs.
When you pour salt onto a slug the salt dries out the slugs body and dehydrates the slug.
Then as the salt dehydrates the slug it dies because of dehydration.
Salt is an easy home remedy to get rid of slugs as you just pour the salt onto the slugs body and although it will take a few hours or so the slugs will die.
The slug needs moisture in it's body to survive and when you dehydrate that slugs body they cannot survive or replace the lost moisture fast enough.
I have poured salt on slugs and it does work great to get rid of the slugs when they are unwanted.
I'm not one for killing creatures but slugs can be a nuisance when they are in your yard around the house and when they come into the house.
If the slugs stayed outside away from my house and outside my house then they would not be killed.