No doubt a small car tire works and so does a big tree stump.

Here is a few sledgehammer exercises you can try:

Exercises where Tire is Flat

2 Hand Overhead Slams
1 Hand Overhead Slams
2 Hands Slide to 1 Hand Overhead Slams
2 Hand Rotational Slams
1 Hand Rotational Slams
2 Hand Rotational High to Low Slams

Exercises Where Tire is Standing
2 Hand Rotational Baseball Bat Swings
1Hand Rotational Baseball Bat Swings
2 Hand Rotational Posterior Swings
1 Hand Rotational Posterior Swings

Without Tire

Acceleration / Deceleration Series

What is the Deceleration Series?
Start of movement – explosive power, followed by immediate deceleration of the implement. Builds mind/body connection, antagonists and synergists statically to decelerate the motion initiated by the prime movers, dynamic grip strength. The goal is to not let the sledge touch the ground after exploding into the movement as hard as you can.

Exercises Without Tire

Golf Swings
2 Hand Baseball Bat Swings
1 Hand Baseball Bat Swings
2 Hand Overhead Decelerations
1 Hand Overhead Decelerations
2 Hand Rotational Decelerations
1 Hand Rotational Decelerations

Levering Series

1 Hand
Ulnar - Front Lever
Radial - Back Lever – “Weaver Stick”
Multi-Directional Levering

2 Hand
Conans – “Halos”
Ulnar - Front Lever
Finger Walking

Multi-Directional Levering
1 Hand
2 Hand