The option that best completes the gap is "waiting".
The full sentence would be: "Do you mind waiting another hour or two?"
The word "mind" in this context means to be bothered or to have an objection to something. In this case, the speaker is asking if the listener would be bothered by waiting for another hour or two.
The verb "waiting" is the correct form to use after "mind" because it functions as a gerund, which is a verb form that acts as a noun. In this sentence, "waiting" is the object of the verb "mind".
Option "wait" is not correct because it is an infinitive form of the verb and doesn't fit grammatically with the sentence structure. Option "to wait" is also an infinitive form and doesn't fit as well as "waiting" in this sentence. Option "to have waited" is a past participle and doesn't fit the tense of the sentence.