I have no idea why you would ask this, but.......
Without oxygen they will be dead within a few seconds, but note that even dunking them in water will not deprive them of oxygen straight away - the oxygen stuck to their exoskeleton is enough to keep them alive for hours.
Dust mites and bed bugs are related to the spiders. Dust mites are harmless except to people who have respiratory problems. Bed bugs sip a few drops of blood from their host and frequently activate an allergic reaction, they have also been blamed for spreading hepatitis in some cases.