Do scriptures mention Vyasa as a Brahmin? What are those specific verses in which he has been described as a Brahmin?
According to Vajrasuchika Upanishad, One is not a brahmana because he/she isborn to a brahmana.
तर्हि जाति ब्राह्मण इति चेत् तन्न । तत्र जात्यन्तरजन्तुष्वनेकजातिसंभवात् महर्षयो बहवः सन्ति । ऋष्यशृङ्गो मृग्याः, कौशिकः कुशात्, जाम्बूको जाम्बूकात्, वाल्मीको वाल्मीकात्, व्यासः कैवर्तकन्यकायाम्, शशपृष्ठात् गौतमः, वसिष्ठ उर्वश्याम्, अगस्त्यः कलशे जात इति शृतत्वात् । एतेषां जात्या विनाप्यग्रे ज्ञानप्रतिपादिता ऋषयो बहवः सन्ति । तस्मात् न जाति ब्राह्मण इति ॥५॥
5. Then is a class the brAhmaNa ? No . Since many rishis have sprung from other castes and orders of creation - RishyashRi.nga was born of deer; kaushika, of kusha grass; jAmbuka of a jackal; vAlmiki of valmIka (an ant-hill); vyAsa of a fisherman's daughter; gautama, of the posteriors of a hare; vasishtha of Urvasi (a celestial nymph in the court of Indra); and agastya of a water-pot; thus have we heard . Of these, many rishis outside the caste have stood first among the teachers of divine wisdom; therefore a class is not the brAhmaNa.
*तर्हि को वा ब्रह्मणो नाम । यः कश्चिदात्मानमद्वितीयं जातिगुणक्रियाहीनं षडूर्मिषड्भावेत्यादिसर्वदोषरहितं सत्यज्ञानानन्दानन्तस्वरूपं स्वयं निर्विकल्पमशेषकल्पाधारमशेषभूतान्तर्यामित्वेन वर्तमानमन्तर्यहिश्चाकाशवदनुस्यूतमखण्डानन्दस्वभावमप्रमेयं अनुभवैकवेद्यमपरोक्षतया भासमानं करतळामलकवत्साक्षादपरोक्षीकृत्य कृतार्थतया कामरागादिदोषरहितः शमदमादिसम्पन्नो भाव मात्सर्य तृष्णा आशा मोहादिरहितो दम्भाहङ्कारदिभिरसंस्पृष्टचेता वर्तत एवमुक्तलक्षणो यः स एव ब्राह्मणेति शृतिस्मृतीतिहासपुराणाभ्यामभिप्रायः अन्यथा हि ब्राह्मणत्वसिद्धिर्नास्त्येव । सच्चिदानान्दमात्मानमद्वितीयं ब्रह्म भावयेदित्युपनिषत् ॥९॥"
9. Who indeed then is brAhmaNa ? Whoever he may be, he who has directly realised his AtmA and who is directly cognizant, like the myrobalan in his palm, of his AtmA, that is without a second, that is devoid of class and actions, that is free from the faults of faults of the six stains (hunger, thirst, grief, confusion, old age, and death) and the six changes (birth, existence etc), that is of the nature of truth, knowledge, bliss and eternity, that is without any change in itself, that is the substratum of all the kalpas, that exists penetrating all things that pervades everything within and without as AkAsh, that is of nature of undivided bliss, that cannot be reasoned about and that is known only by direct cognition . He who by the reason of having obtained his wishes is devoid of the faults of thirst after worldly objects and passions, who is the possessor of the qualifications beginning with sAma (dama, uparati, titikShA, samadhana, sraddha), who is free from emotion, malice, thirst after worldly objects, desire, delusion, etc., whose mind is untouched by pride, egoism, etc., who possesses all these qualities and means- he only is the brAhmaNa. Such is the opinion of the veda, the smritis, the itihAsa, and the purANa-s . Otherwise one cannot obtain the status of a brahmaNa . One should meditate on his Atma as sachchidAnanda, and the non-dual brahman . Yea, one should meditate on his Atma as the sachchidAnanda brahman . Such is the upaniShad.
So,VedaVyasa was a self realised Brahmana and an excellent teacher (Guru) like every other rishis on that verse.
I hope this clarifies your queries.