My child clenches his teeth and holds his breath when he gets angry. Is this normal?

Ignore It. The purpose of a tantrum, even involuntary, is to obtain a goal. Ignoring it teaches the child that this action gains no reward. Even if they turn blue!! The brain will naturally protect the child from damage. When done, give them a hug, reinforcing the "good " behavior. Over a period of 2-3 weeks, if consistent, the tantrums will lessen in frequency and severity.
The point of anger.. ...Is to get you to change what you are about to do. Children will often repeat behaviors that have successfully got your attention in the past - which, i would guess, included a fairly significant reaction to clenching teeth. Breath-holding may actually be natural, as a consequence of hyperventilation while screaming.
Tantrum varient. You are describing a tantrum varient of childhood loosly called "breathholding spells".Rare but occasional in infants it peaks around 2 & fades by school age in most.Often triggered by a scolding or your refusal to comply with their requests, they can turn blue, pass out & twitch.It is not a seizure & they self recover.Avoid locking eyes but monitor them.Don't reinforce the behavior by cuddeling.