Is it safe to competely cut out sugars and carbs on a diabetic diet?

Absolutely - Debated. Almost impossible to do 100%. But if sugar is high, adding more doesn’t help. Like other animals, in healthy condition, ?50% of internal sugar is from internal conversion of protein ; fat into sugar. Converting fat to sugar also generates soluble ketone compounds; another alternative fuel. Brain ; nerve cells burn sugar ;/or ketones for energy to function; reason too low a total creates problems.
No. The body needs healthy low glycemic carbohydrates. Eating too little carbs can stress the body and in the long run worsen Insulin resistance.