In Red Alert 2, the American GIs (which were very plentiful from airdrops) could dig in and wipe out most tanks. And as soon as they got a armor kill, they would rank up quickly and have insane range and damage.
So maybe between garrisoning rifleman and missile dudes, as well as putting them in the little foxhole things the rifleman can build, you probably have a cheap but decent defense against mammoth tanks. I'm not sure how good the mammoth are at infantry in this one, but in previous games, all those big tanks sucked (except for the mammoth missiles, or run them over with force-move) again dug in infantry. They got tore the hell up. So if you don't have any tough vehicles to counter them, I'd try a combo of well-placed infantry types.
edit: I played the two campaign missions on medium. They put up a quite good fight but I had no problem taking them out after I got built up with a lot of units. I've played C&C 1 since 1996 (had the demo earlier but my computer ran it at like 2 fps), plenty of RA, then Tib Sun, then lots of RA2 (got in the top 75 on WW Online in 2001-2002), so I have a ton of C&C experience in single and multi.
Yet skirmish on normal for the first time and I got wrecked. I wasn't out yet, but from the stats when I quit, they were so far ahead, and I had lost my tib refinery twice, had to sell my tech center, lost my war factory once, etc. Fvcking superweapons!!
Those suicide guys Nod sends suck too.
I think with a couple more times I could take them out on normal, but even as a C&C veteran (played them on and off for 10 years), I don't think I could do hard and certainly not brutal.
Also, the pressing 'n' or 'g' on my or the computer's side didn't change them.