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