Oxford say mostly demolition. Making it harder for the enemy to advance. Mine fields, obstacles, destroying roads and bridges but the flip side is to prevent the enemy.from doing the same. Neutralizing enemy.mine fields, destroying their obstacles preventing them from destroying roads and bridges.
Sapper in WWII would have used Bangalore torpedoes to cross wire obstacles or satchel charges to take out a bunker. these days we tend to go with.more stand off weapons though we do still have Bangalore torpedoes.
Combat Engineer can build fighting positions for tanks to taking out bridge abutments but Sapper would be more along the line of smaller explosives and mines, and going in and clearing rooms/buildings of boobytraps and explosives.
A combat Engineer is a Sapper. I should know, I am one. (B Co 31st Engr Bn Ft. Leonardwood, MO, C Co 16th Engr Bn Erlangen, DE(deployed to SWA in 1993), B Co 82nd Engr Bn Bamberg, DE(deployed to BiH in 1997)).
A Combat Engineer is the most versatile combat soldier in the Army. Not only do we have a primary duty which was posted above(including bridge building, road building and runway building), we are also take on many Infantry tasks. Attack, patrol, defense, escort, etc.
Our primary mission in SWA was to provide security for several Patroit sites.
In 1995, my former unit deployed to Croatia/BiH and built the bridge across the Sava River the Task Force used to cross into BiH. It was the longest floating assault bridge in military history.
When I deployed to BiH in 1997, our mission was to supervise and support the local military in removal of the millions of mines that were laid in Bosnian War.
And yes, we still use Bangalores. Even make field expedient ones from pickets and C4.
First in, Last out. Steel Sappers!