You are probably:
I start out quite skilled
Not quite sure about this line but I'll take a guess: Wars start of something massive and infamous like how World War 2 started with the assassination of a world leader, what some could say a "skilled" mission.
Throughout the nation I've drilled,
It can "drill" fear into the hearts of civilians and world leaders. Never mind, how about EVERYONE!
I'm sexist to the extreme,
In wars, soldiers are mostly known as men. In the past, soldiers were only men not women.
You'll soon know what I mean,
When you get older, you will soon learn that most previous wars had mostly or only men.
Your children should thank me,
Modern children just love violent and action-filled games, especially related to war... PG-13!
Your wife might just hate me.
As said about being sexist to the extreme, the wife of a soldier will be very sad if she lost her husband in war.
Knives I despise
Not quite sure, but soldiers usually go hard-core, and long-range battles with airplanes, naval ships, guns, bazookas, pistols... Do I need to go further?
I hide from your eyes.
You can't see war itself really.
Avoid mutations, // From your medications.
In serious, dangerous wars, some countries might go too far and try to go with mutated, superhuman soldiers. Or maybe the world's most dangerous "superhero".
So we will do all your tests,
In wars, countries "test" each other to see who wins the battle and then the war. The "winner(s)" of the "test" will win the war and many more battles.
But eventually we'll both rest.
One side shall surrender or lose to the other, stopping the war and letting the countries and people "rest in peace" (I'm not talking death here).