To pause a block-break, you must do the following:
1. Start breaking the block
2. Hold down right-click
3. Release left-click
4. Hold down left-click
5. Release right-click
Once this series of button presses is done, you are able to block while breaking to pause the breaking (works with all things with right-click functionality).
SECONDARY BUG! If you move your mouse over other blocks whilst using the block button, the animation will stay in place. Moving off all blocks and releasing both attack and block will keep the animation at its current state. You are then able to continue breaking the block by holding down right-click, hovering over the block, holding down left-click and then releasing right-click (Images may help show this)
Images (in order):
1. Shows blocking pauses animation
2. Shows secondary bug
3. Shows secondary bug
4. Shows eating pauses animation
5. Shows powering up bow pauses animation
Confirmed in 1.8.4.