In plain words
Yogins perform action with body, manas, buddhi, and even the senses, each free of any sense of ‘mine’, abandoning attachment, for the purification of oneself.
Word for word
With the body, with the manas, with the buddhi, even with the senses, [all] free of 'mine', the yogins perform action, having abandoned attachment, for the purification of the self.
The commentators
Bhagavadgītābhāṣyam
यस्मात् —
कायेन देहेन मनसा बुद्ध्या च केवलैः ममत्ववर्जितैः ‘ईश्वरायैव कर्म करोमि, न मम फलाय’ इति ममत्वबुद्धिशून्यैः इन्द्रियैरपि — केवलशब्दः कायादिभिरपि प्रत्येकं सम्बध्यते — सर्वव्यापारेषु ममतावर्जनाय । योगिनः कर्मिणः कर्म कुर्वन्ति सङ्गं त्यक्त्वा फलविषयम् आत्मशुद्धये सत्त्वशुद्धये इत्यर्थः । तस्मात् तत्रैव तव अधिकारः इति कुरु कर्मैव ॥ ११ ॥
In plain words
Because —
'By the body' means just that; 'by the mind and intellect'; and 'the mere,' meaning empty of any sense of 'mine,' thinking, 'I do this only for the Lord, not for a fruit of my own'; 'the senses too,' empty of that same claim of ownership — the word 'mere' really applies to body, mind, intellect, and senses alike, wherever it appears, so that no sense of 'mine' creeps into anything they do. 'Yogins' — those still engaged in action — 'act,' having let go of attachment to the fruit, 'to purify the self,' meaning to purify the inner being. That's the meaning. So your own right and duty is exactly there, as already said — simply act.
Close to the Sanskrit
Since —
'By the body' — by the body; 'by the mind and the intellect'; 'and by the mere' — devoid of any sense of 'mine,' thinking, 'I do this action for the Lord alone, not for my own fruit' — 'the senses too,' empty of any notion of 'mine' — the word 'mere' is to be construed respectively with 'body' and the rest also — so as to exclude any sense of 'mine' in every operation. 'Yogins,' those engaged in action, 'perform action,' having abandoned attachment regarding the fruit, 'for the purification of the self,' [i.e.] for the purification of the inner being. That is the meaning. Therefore your entitlement lies exactly there, as was said — so do action alone.