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Your father is diabetic must be taking medicines for diabetes
and blood sugar is 106 mg/dl, If tooth is in bad condition and can not be saved by any conservative procedure then yes they can be safely removed under proper antibiotics cover to prevent infection to spread and complication.You can get extraction as early as possible.
He should continue antibiotics and analgesics as advised by doctor.
Any space created by teeth removal should be replaced with artificial one once healing is complete.