Can words be removed from language? Are there examples of such?

There is no single "English Dictionary". A simplified dictionary or a learners' dictionary that has only commonly-used words will certainly have new words added and old-fashioned ones removed from time to time. However a comprehensive dictionary such as the Oxford English Dictionary https://www.oed.com/ only gets bigger as time goes on and new words come into use.

Have you heard any of these words: "ambassade", "latrant", or "princox"? Despite all of them occurring in Samuel Johnson's 1755 dictionary, it's very likely you haven't. If listed in dictionaries (they aren't in NOAD), you will see them listed as archaic, which means that nobody really uses them anymore. In other words, they have essentially been removed from the language. As you go back further and further in time you'll see more and more words like this, especially with Old English.

As for whether dictionaries remove words, that depends on the dictionary. For print dictionaries, the answer is almost always yes, words are removed. The notable exception was the Oxford English Dictionary, when it was in print, because it is, in part, a historical dictionary. In addition, online dictionaries don't tend to remove words, since there's not much cost and some potential benefit to keeping them. The policies for adding/removing words for both the OED and Oxford's main online dictionary can be found here. In contrast, see this article to see their philosophy about their printed children's dictionary and this article for a discussion of what words they removed from the Oxford Concise English Dictionary (every year it's discussed because people get upset about it).