Thank you for contacting AaE for help.

I'm assuming you want to keep the plant from getting bigger topside which is what will happen if you split it because Spathiphyllum wallisii or Peace Lily would be perfectly happy being rootbound.  At the point where there's nothing but roots in the pot then it becomes absurd.

To split your plant make sure the plant has been watered recently and the potting medium is damp but not soakingj (you might have to wait a day or so after watering).  Carefully remove the rootball from the pot and gently lay it down without damaging the foliage.  First, try to grasp the foliage stems at the level of the soil half in one hand and half in the other hand and try wiggling the root ball apart to separate the roots of each half.   If that doesn't work, sterilize a very sharp knife then cut the rootball in two all the way through and down to the base where you believe is a good dividing point.  It'll get messy so you may want to lay newspapers down on the floor before attempting this.

Pot each half in pots of the same size that the plant was in before making sure each new rootball is centered and at the same level in the potting medium as before.  I would suggest using fresh potting soil that's been recently moistened.  Place the plants in the same environment as before and water.  Resume your usual watering method which (since it's spring) is more frequent than in winter because it should be entering its active growing period. 

Spring is a great time to divide houseplants because most are entering their active growing period with the longer days.  Your new plants may not appear to be doing much for awhile because they will be settling and growing their roots into the new spaces of the pots.

Another option if you only wanted one plant, is to root prune it and repot in the same pot with fresh potting medium.  This will rejuvenate the plant but keep it about the same size.  To really keep it at the same size some topside pruning may be needed.

I hope this helps.