Thanks for reporting your bug encounter.
In your first list of errors, the top one is the actual problem. The other messages are just bubbling up from the source of the error to provide some more context. The Maya API command "dgMod.deleteNode(zTissue4); doIt()" failed. That's a strange failured to have. Does a zTissue4 object exist? Is it one that you were trying to delete? Despite this failure, did it actually still get deleted? Does it happen reliably for you? I played around a little bit, but wasn't able to reproduce this.
For your second set of error messages ("zEmbedder1 - No tet mesh geo data at index 99"): the zEmbedded node has iGeo and iGeom array attributes attributes that have to be in sync. If you delete the zTissue or other Ziva nodes associated with a tissue, you probably break a connection to iGeo without breaking the corresponding connection to iGeom. You need to do both and make sure that all of the other connections don't change index. The iGeom connection is part of the Maya deformer system, and changing it "properly" is the stuff of nightmares, as you probably know. This is part of why we have a deletion command in the first place -- there's no way to get Maya to do the right thing here without running our own code. Other connections also need to be broken to the zSolver node. I don't recommend trying to do this manually.
For the record, I'm tracking this with ticket "DEV-311".