まだ is an adverb which indicates that the action has not yet been completed. Here, the sentence ending is negative. This pattern can be used as a negative reply to the question もう Ｖましたか. The same meaning can be expressed by simply saying (いいえ、) まだです without using the verb. It should be noted that the meaning could be something like "I am not going to do ～ yet; I do not intend to do ～ yet" when volitional verbs are used in the "まだ Ｖません" pattern.
・Volitional verbs refer to verbs which express actions one has control over(e.g., のみます[drink], いきます[go], おきます[get up]).
・Nonvolitional verbs refer to verbs which express actions one cannot control(e.g., わかります[understand], はじまります[begin], the subject being a thing, おわります[be over/come to an end]).
A: しごとは もう おわりましたか。
B: いいえ、まだ おわりません。