Translation:Don't close the door.
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No. 不要 means "do not". It is imperative, and it is stronger (paints the action in a more negative light) than 别. Note how there is no stated subject in this sentence (just as most English imperative sentences don't have a stated subject). If you want the characters 不要 to mean "do not want", you need to state the subject who is "not wanting". Also, when 要 on its own means "want", it is usually followed by a noun, whereas an imperative needs to be followed by a verb (what needs to be done/not done). If that feels to confusing, you can use 不想要 to unabiguously mean "do not want". 想要 can be followed by a verb or a noun. 想 followed by a verb means "to want". 想 followed by a noun means "to miss".
I learned from my teacher that 别 (Bié) [= "Do not"] is just an abbreviation of 不要 (Bù yào); not that 不要 is stronger.
Maybe there is a difference in usage, as I read from zhouhuanyue's comment: "別 is used if the person saying it thinks no one has done it yet, 不要 is more like "stop, or "don't (do it)". We can possibly deduce from this that 不要 is (a little?) stronger.