Hello Summersunshine,

Yep, it is possible to eradicate mites.

First, isolate your Croton, ASAP.

There are several ways to eliminate mites, either by using chemicals or organic methods.
I prefer the latter.

Here's my home-made insecticide recipe and method.

Soak entire plant in a tub of soapy water. Let it sit about 5-minutes.
Rinse with clean water.
Wash tub and area thoroughly after use.

2-3 drops dish soap. Lemon peel or juice. Garlic. Hot pepper. Listerine, 'generic will do.'

Allow above ingredients to sit overnight. The following day, every part of plant/s are sprayed from trunk to foliage.
Usually one application is sufficient, but in major cases, plant/s get a double dose, 3 days after first spray.

This mixture won't spoil. When I had the energy, lol, I'd spray my plants twice a month..Believe me, it works.
Notice, no harmful ingredients, so it's safe if one has children or pets, plants and ourselves.

Good luck, Toni