Teamwork is a good thing, considering that's a core mechanic of the game, i don't really think that's a problem.
The Mammoth tank is supposed to be the most powerful unit in the game, period. And so, you would expect it can take out multiple (two or three) vehicles before succumbing to enemy fire, and for the amount you pay for it, you'd expect it to be.
Player skill apart, you cannot expect to go one on one with a mammoth and come out on top, it shouldn't work that way (unless you're a flame tank licking the mammy).
As a stank, you don't engage directly do you? You'd flank one if you attack it.
And as an Arty, you wouldn't use it as a main battle tank would you? It's a support unit, you're best to try and out range it.
In response to your suggestions:
nerf overall dmg and reduce max. range (esp. on Heroic)
Again, it us supposed to be the most powerful unit in the game.
That being said, it's missiles aren't really that strong, and can be dodged easily by nimble units on sloped terrain.
The cannon should be powerful to compensate for it's sluggishness and poor maneuverability.
Enemies (unless in number) should be weary when trying to engage one. Making it weaker would negate this completely.
As for it's range, it's only slightly longer than the medium and light tank, if even that, it could be equal to them both.
reduce mammoth tank HP
This coupled with it's already low speed means it will die faster. Being slow and more fragile = a useless paperweight, you'd be dead before you can even get halfway across the map.
If you're wanting to nerf it's health, then it's speed would need to be increased accordingly. Less armour = less mass = more speed and maneuverability
make mammoth tank slower
It's slow enough as it is, and can easily be sniped by an out of range arty, not to mention enemy infantry can very easily run up to it and throw timed c4 on it.
less shots per minute
This is essentially just damage output again, see first point on damage.
In relation to having repairs behind a mammy, then it should be harder to destroy, just like it is with any other unit.
Remember, this is a team game and it's hard enough to get someone to follow behind for repairs as it is.