I am currently f1 student. Can i work with the SSN "valid for work only with DHS authorization"?

You need separate authorization, just as the card says. Either OPT or CPT most likely. You need an SSN to be able to work in this county, even with an SSN. - so if you are work-authorized in the future you already have the SSN; that's the benefit.

do you have work authoirzation? No, then you cannot work.

I would check with your school to see if you qualify for OPT or CPT if you wish to work off-campus. If you work without valid authorization you will be at risk later.Just because you have an SSN does not permit you to work off-campus without valid authorization.