As has been pointed out, it's not a great idea to just pick someone up and chuck them over your head - it's much better to use momentum, both theirs and your own. In order for a reasonably sized mammals to do this, the best bet would probably to launch themselves at each other from a distance of, say, $1$m, for some explosive power into each other, such as here, at which point each would try to turn (for increased angular momentum) and fling the other into the direction that it's already facing, requiring technique, timing (OK, this is just technique again) and a bit of strength (though maybe not as much as you'd think). While the linked video shows one of the tigers leap vertically, they would probably stay on the ground and 'ground' themselves to the Earth in order to change directions of momentum more efficiently. 160
(also, 1m is small enough that if it doesn't work the first time, they can just keep going at each other)
The point of this is that the 2 mammals move towards each other and connect, at which point the better fighter (the one that wins) transfers its momentum to the other by the process of turning its linear momentum into angular momentum and back into linear momentum of the other person - a bit like a bigger version of this moment, only with more movement involved - note the way that the woman twists herself to the side in order to get that conversion of momentum in.
If this was an actual fight, they would both grapple instead of throwing at this point for a short time, but that would negate the initial linear momentum of both of them, and the point isn't to fight, but to get the biggest throw.
Chucking in some maths:
You want the mammals to throw a distance of around $5$m (for ease of numbers), most the power of which would come from the initial 'leap towards each other' bit.
Assuming this to be the case, using the standard constant acceleration equations with final velocity $v = 0$ at the highest point, initial velocity $u$, acceleration $a = -g$ (due to gravity) and vertical displacement $s = 2.5 \tan\left(45\right) = 2.5$ when 'thrown' at an angle of 45 degrees; $v^2 = u^2 + 2as$ (in the vertical direction, immediately after impact of the mammals), the initial vertical velocity would be required to be $\sqrt{5g}$.
For this to happen, the horizontal velocity would also be equal to this (due to being 'thrown' at an angle of 45 degrees). Assuming that the change of direction of momentum is 100% efficient (or extra strength could be used to help this) and ignoring friction, each mammal begins with a momentum of $mu = m\sqrt{5g}$ and a kinetic energy of $\frac{1}{2}mu^2 = \frac{5}{2}mg$ Joules, which is also half of what the looser ends up with, to conserve momentum and energy.
In order to get to this speed over the distance of $s = 1$m, from the above equation with $u = 0$, $v = \sqrt{5g}$, you want an acceleration of $\frac{5}{2}g$ m$s^{-2}$, giving a force of $F = ma = \frac{5}{2}gm$ N, or being able to accelerate at about 7.5 times <PERSON>.
At a bit of a guess, evolutionary adaptions would be reasonably strong hind legs and something a bit similar to elbows in the front legs. On top of this, they would need to be able to survive impacts of $5mg$ Joules at wherever they land (probably either on the back or legs).
To be thrown an arbitrary distance, $d$, you want an acceleration of $\frac{1}{2}gd$ m$s^{-2}$, or $\frac{3}{2}d$ times <PERSON> acceleration (for an acceleration due to gravity equal to that of Earth) 771