Can a diabetic eat beef or pork liver with it causing blood sugar or blood pressure going high?

Yes: Yes, meat does not contain carbohydrates/sugars, so it does not raise the blood sugar. It should also not affect the blood pressure. Foods don't generally affect blood pressure like that. Usually, if they do, it's due to a high amount of sodium in the diet rather than what a person is actually eating, so, in that case, switch to a salt substitute or cut out salt as much as possible.