In my experience the phrase dry off (as opposed to dry it off) is generally used (intransitively) when evaporation serves to dry a person/creature or object, as in:
Give me a few minutes to dry off after my swim.
Make sure that the dog dries off before it comes inside.
Leave the umbrella outside to dry off.
Hang these clothes on the line; they will soon dry off in the sun.
although the off is optional in the last two examples.
It is also optional in the following examples in which the phrase is split:
Dry yourself off with this towel.
Dry the car off with the cloth.
Dry - without off (whether adjective or verb) can be used in any context. Often, it's just a matter of choice.