Yes, it looks out of place there.

Def the wrong place for it.

I would turn it so it's landscape and put it over the fireplace. The painting is much too large for the proportion of the fireplace.

Before I even read the question I looked at the picture and thought, "that mirror needs to go" so yes, get rid of the mirror. I don't agree with chelsea about hanging it over the fireplace though, since you have high ceilings in the space it would be too small in scale. Try actually hanging the art above the mantle about six to eight inches instead of just resting it on the mantle. Then try to resist the urge to put a ton of stuff on the mantle. Best of luck!

I've commissioned a large landscape to go over fireplace. The abstract there is just temporary. I always meant to get it hung but was never crazy about it. Thanks for comments on mirror. It's going.