The answer to this question depends on which Oxford dictionary you’re talking about. For OED.com (and its earlier print editions), the answer is words are never removed. For their other online dictionary it’s just rare to have words removed. And in print dictionaries, the answer is yes, words are often removed for space reasons when new ones are added. (See here for example.)
This is said in their FAQ:
Once a word is added to the OED it is never removed; the OED provides a permanent record of its place in the language. The idea is that a puzzled reader encountering an unfamiliar word in, say, a 1920s novel, will be able to find the word in the OED even if it has been little used for decades. As words, or senses of words, fall out of use, the OED marks them as rare or obsolete, but does not remove them.
Although oxforddictionaries.com is a record of current language, it doesn’t generally remove words. As an online resource, it is not constrained by physical print dictionary size and can include an ever-increasing number of words, phrases, and senses.
Our print dictionaries are designed to be as up-to-date as possible, and are frequently revised. Due to space constraints, however, we may remove some words which are perhaps no longer in common currency but where possible, we try to save space by design tweaks rather than removing words.