Delete all documents from index/type without deleting type

I believe if you combine the delete by query with a match all it should do what you are looking for, something like this (using your example):

curl -XDELETE 'http://localhost:9200/twitter/tweet/_query' -d '{
    "query" : { 
        "match_all" : {}
    }
}'

Or you could just delete the type:

curl -XDELETE http://localhost:9200/twitter/tweet

Note: XDELETE is deprecated for later versions of ElasticSearch

The Delete-By-Query plugin has been removed in favor of a new Delete By Query API implementation in core. Read here

curl -XPOST 'localhost:9200/twitter/tweet/_delete_by_query?conflicts=proceed&pretty' -H 'Content-Type: application/json' -d'
{
    "query": {
        "match_all": {}
    }
}'