Yes, spider-mites are deadly to VFT they will be present on the plant
and on (in?) the surrounding soil and can be removed by soaking
the plant underwater for a couple of days. This treatment will
work and the plant should be kept in the sun for it. The eggs
are in the webs. These will not die so a repeat (or several)
will be needed. Also, you can spray the plant with soap. Keep
it out of the sun if you do this and wash the soil after with
water. This will not kill the eggs either. Has it showed any
sign of weakening? Usually you will see this if the mites have
become numerous enough to start making nests.
Dave Evans