Learn French: Nous recyclons plus de déchets que vous pour sauver la terre. - We recycle more waste than you to save the earth.

Because we are comparing amounts of a noun. To say "more [noun]", you must use plus de. If you were comparing adjectives (like saying someone is "more intelligent"), you would just use plus without the de.

Since déchets is plural, why isn't it plus des déchets?

Expressions of quantity like plus de (more), moins de (less), and beaucoup de (a lot) have a fixed de. It never changes to des, even if the noun that comes right after it is plural.

Do I pronounce the "s" at the end of plus in this sentence?

No, the "s" is silent here. When plus is used in the expression plus de to compare nouns, you generally drop the "s" sound, especially since the next word (déchets) starts with a consonant.

Why is "to save" translated as pour sauver instead of just sauver?

In French, when the English word "to" actually means "in order to" (showing the purpose of an action), you must use pour followed by the infinitive verb. You are recycling in order to save the earth.