Yeah you can redstone to it, here I made you a screenshot.

1. You can power the mortar from where any of those redstone repeaters are.
2. You need a redstone torch under it, like you can see above.
3. A chest with projectiles and gunpowder can be put at any of the 3 sides where the normal torch is not, so that chest could be either side of the mortar.

You can load both projectiles and gunpowder into the chest and flick that lever and itll, load, fire, load, fire etc. Also listen to the sounds, it makes a sound when its empty, a sound when it loads and a sound when it fires (That last one is obvious haha)

Hope this helps.