If no info on the labels, contact the manufacturer.

Why?
Copper is most often used for control of algae or fungi and is a very toxic, to you, material. Then copper is most often used as a dormant spray or dust and spider mites are mostly a growing plant problem.
Neem Oil products alone are broad spectrum poisons that can also kill off any predators of spider mites. Understanding the life of a spider mite can help you with control without using very toxic poisons.

Here is a link that might be useful: About Spider Mites

Copper is an acceptable organic fungicide, when used properly and with due care. However, mixing of any materials should never be done unless careful research says it is okay to do so. In some instances mixing two chemicals has resulted in one being rendered ineffective and in others a much more potent substance has been produced.
Is copper the right substance to control your leaf rust? What do the growing conditions contribute to that problem? Can a change in growing conditions solve the problem rather then some toxic chemical?

Here is a link that might be useful: About organic cides

I found this while googling. Even though this is old, I think this needs to be corrected. Copper is not toxic. Your body requires copper to function (recommended 2 mg per day). In excess, copper can cause you to become sick. Consider this. That's 2-8 mg per ounce depending on application. Then consider how many ounces end up staying on the fruit. Far less than an ounce. Then consider that the rain often rinses enough off that you need to reapply after a good rain. And you should be cleaning your produce before you eat it. Copper is perfectly fine to use.

To correct some faulty information in this old thread, I'd like to say Neem oil and horticulture copper can safely be used in a single tank mix. Both products are acceptable by the OMRI.

Be sure to read and follow the directions on each label carefully.

Use caution though when using in warmer weather as neem is an oil, copper a heavy metal. It could possibly cause burning of foliage if used during heat of the day. Not sure if the copper is really necessary since Neem is a fungicide, miticide and insecticide in one.....just saying.

I had fungus this year on several cucurbits. I attempted Neem oil at first and it was ineffective. After applying Copper once per week over several weeks, it started bringing it under control and new leaf growth produced leaves that were free from fungal blotches.

Several years ago, I had rust and blight on a bunch of roses. I tried Neem oil. It did nothing. My roses basically went dormant that year, nearly leafless by the fall and came back the following spring after I manually cleared out all the diseased plant material.

Just because the Neem oil bottle says it is fungicide, miticide, and insecticide doesn't make it the magic cure all. It doesn't always work and other methods may be required for the specific case a plant is having. It requires experience, patience, and trial+error to correct for issues. Check your local extension for integrated pest management to prevent, maintain, and fix your edible and ornamental plants.

There are some things that neem oil does not fix/solve. That is why copper fungicide exists/is used. Yes, there is some overlapping, but both are needed for variety of reasons. I use both annually on my expensive citrus trees as some fungus, once it arrives on your tree, it is usually too late. I have to spray copper fungicide as a preventative measure annually. It isn’t needed every year, but why take that chance.