Can we ignore sense doors through meditation? In the process of reading a book, we need only the mind and the eyes. There is no need of ears and tongue.

In the process of hearing Dhamma,there may no need of eyes.

Are there any meditation practice to ignore senses completely for a period of time ?

(I'm looking for a specific meditation practice designed to achieve this, I know that we can achieve a similar result by doing Ānāpāna/breathing exercises,but may take much time )
One cannot avoid contact (described below) hence one cannot ignore the sense doors totally:



Cha Chakka Sutta



(Samuday’atthaṅgama) Loka Sutta

What one can do it to ensure any contact (described above) does not result in craving and break the above progression of events at feeling. This can be achieved through meditation.

See 


Food and other cravings, and guarding the senses
Rejecting clinging to both pleasure and displeasure
How should I watch sensations in Vipassana meditation?
Sankhara meditation
Meditation technique to reduce/control pain/sorrow/loss 


answers for more details.