If you don't have access to specialized gear, you can perform several combat engineering duties with far more common weapons.
Minelaying can be performed by any LRM rack or artillery piece.
Minesweeping can be performed by any artillery piece, as well as most large missile racks, even without using Mine Clearance Missiles.
Any weapon capable of dealing damage can bring down a structure given enough time, but most players are concerned with doing the job quickly, so big damage is the order of the day. AE weapons can do the job very quickly, but hazardous if you care about preserving buildings next to your target. Big MRMs are actually a pretty good way to reduce a building quickly and cheaply, especially since the immobile nature of most buildings nicely offsets their to-hit penalties.
Digging holes can be accomplished in the same way as collapsing buildings, though the sheer damage required means you really want the multiplier AE brings. A few well-placed Long Tom shells are the key to transforming a sheer cliff side into a rough but traversible slope.
Any missile rack loaded with frag missiles can be effective at clearing trees, but like all of the above, more/bigger is better. A JES I is actually a pretty decent weedeater.
Looking at all of the above, there's a reason why when designing my SLDF Combat Engineers infantry company, I attached a pair of LRM Carriers to those platoons. :thumbsup: