As fusiliers with the Doctor skill, a Trauma-Doc's offensive abilities consist of a BS12 Combi Rifle and an emergency knife for if something engages them in melee.
Finish off Unconscious enemies in locations an enemy doctor can reach. Coup De Grace them if you've got a trooper close enough, or simply keep shooting them.
Using weapons which do more than one wound in an order (either high Burst or DA/EXP) helps reduce the chance of an enemy being able to fall Unconscious behind waist high cover, safely out of sight. If they do, Speculative fire can help finish them, since Unconscious models can't Dodge.
Either hunt down and kill the Doctor, or stop them reaching their patient. A doctor positioned behind the same piece of cover as a likely patient may be vulnerable to a template hitting both models.
If you really need a target to stay down; and can't finish it; Immobilizing or Isolating it after knocking it Unconscious will require an Engineer to reach it AS WELL, which will at minimum cost your opponent extra orders.
The more valuable the troops you have (with Wounds rather than Structure), the more a doctor can benefit your force. Being able to revive an Auxilia may be useful, but bringing a Nisse or Swiss Guard back into the fight can be game winning. Consider what in your list would be worth spending the orders to reach and revive: a sniper in your own Deployment Zone 2" away from your doctor is less of an investment to reach, and so more likely to be worth Doctoring, than a Montesa Knight on the far side of the table.
Consider taking a Palbot or two, they'll prevent your doctor taking part in Coordinated Orders but their effect is almost like having additional doctors. They are also faster, more expendable and situationaly sneaker than their doctor; making them particularly suited to reaching patients out of easy reach.
Active Turn Role
A Trauma-Doc can ARO like any other rifle wielding troop; covering horizontal lines and your own deployment zone against warbands, Impersonators and Aerial Deployment. Generally a Trauma-Doc is one of your more valuable support models however, so its ARO duties shouldn't be particular risky.