In aikido as in other aspects of life, breathing is important. You want to be exhaling as you hit the floor to absorb some of the impact and inhale to push yourself back to standing. You would also want to exhale on the throw to gather the breath power/ki and put it into the throw.
In making my way through changes in my life both in the recent past and long time past, I've paid a lot of attention to my breath. Sometimes all I seemed to have the emotional strength to do was breathe. And sometimes that's all I did need to have the emotional strength to do. Breathe and be, be awareness being aware. Sounds all esoteric and bullshitty doesn't it? It's not. It's how I got sober, it's how I stayed sober, it's how I got strong, and it's how I've stayed strong.
Breathe, and be. Then do it again. And because my meditation technique is largely informed by Tibetan Buddhism it's ok while you're doing this to breathe and be and pet the cat, or scratch whatever you need to scratch.