Question: I'm using DSE Search 3.2.1. We have removed some unneeded indexes and fields and posted the `schema.xml` document to all of the nodes. Do we need to do anything else to have it discontinue indexing data? Do we need to run a reindex, or a full reindex?

Answer: 
If you don't reindex, the existing Solr index field values will remain, occupying space and responding to queries. And fresh inserts or updates will not have the deleted fields. As Ben said, that might be okay.

A Solr reindex will delete all of the old field values.
Ideally if you change anything in schema.xml and want the changes to reflect you have to do a re-index. But, doing a re-index totally depends on the application use case and the number of records you have in it. If the reason for removing the index was due to lack of usage then there is no need for you to do re-index since no is going to search on them. The old indexes will take some space but it should be fine. Also, be careful when you are doing re-indexing because it highly depends on the number of documents you have. If you have somewhere around 10M and above I would **NOT recommend** re-indexing as it is CPU & I/O bound operation. If the number of documents are less then you can surely go ahead and do it.