Hmm, where to begin? First off, no, hydrogen peroxide won't hurt plants. Second, and more importantly, it won't do much of anything to cure your spider mite infestation, if that is indeed what you have.
How do you know they're spider mites? Are there web-like things on your plants? The bugs themselves usually look like tiny red or brown specks. They suck the juice out of the leaves, so leaves will show signs of infestation first. If you look at the undersides of the leaves, you'll probably spot other little specks that are their eggs.
If you do have spider mites, then I feel for you. Spider mites are tenacious fuckers and are very hard to get rid of. Most likely, you got them from a clone that already had them on it. I don't know anyone who got them otherwise.
You can control them by washing your plants with plain water, making sure to thoroughly wash the leaf undersides. Do this to every plant in your grow, every other day. I took mine into the kitchen and sprayed them with the sprayer in the sink. This helps, but rarely gets rid of them for good. If you have plants in flower that have the little bastards on them, all you can do is spray regularly to keep them to a minimum until harvest. I suggest Dr. Doom's Spider Mite Knockout. I tried a multitude of products to no avail until I tried Dr. Doom. It has the highest percentage of pyrethrum on the market and pyrethrum is a spider mites worst enemy.
The final solution can only be achieved by removing all plants from the grow and bombing with a pyrethrum bomb. I took clones of the strains I wanted to keep. I then took all of those clones to a friends house who doesn't grow and thus has no mites. My friend checked them 3-4 times daily, killing any mites he saw. In the meantime, I set off a very strong pyrethrum bomb in my grow room. 12 hours later, I opened the room and cleaned everything in it thoroughly. I left the clones at my friends for a week or so, until he was certain there weren't any mites on them. Finally, I brought the clones back home and started everything fresh. I haven't seen a single mite since.