Cascade style delete in Mongoose

In case your references are stored other way around, say, client has an array of submission_ids, then in a similar way as accepted answer you can define the following on submissionSchema:

submissionSchema.pre('remove', function(next) {
    Client.update(
        { submission_ids : this._id}, 
        { $pull: { submission_ids: this._id } },
        { multi: true })  //if reference exists in multiple documents 
    .exec();
    next();
});

which will remove the submission's id from the clients' reference arrays on submission.remove().

This is one of the primary use cases of Mongoose's 'remove' middleware.

clientSchema.pre('remove', function(next) {
    // 'this' is the client being removed. Provide callbacks here if you want
    // to be notified of the calls' result.
    Sweepstakes.remove({client_id: this._id}).exec();
    Submission.remove({client_id: this._id}).exec();
    next();
});

This way, when you call client.remove() this middleware is automatically invoked to clean up dependencies.