In the case of an older plant, an ax or a mattock might be required. However, the chopped-up root system recovers quickly and completely, and the shoots rising from it will be intact. Watering first will soften the soil. If you don't have the strength to do this or can't find an assistant to help, you can reduce the mass of a grass clump by cutting outside stalks periodically. Their ranks include such delicate plants as baby's breath, baptisias, globe thistles, ladybells and lupines.
Peonies suffer grievously or die when their roots are disturbed.
If they must be moved, mid-fall is the time to do it. Thorough watering after planting is a must, and a bucketful of superior soil helps the young plant to get established. As always, the odds for the success of a division or a transplant will improve dramatically when the weather is cool and cloudy.