client.js

var insert = function (data, callback) {
  console.log('fail', data);
  callback();
} 

var update = function (data, callback) {
  this.insert(data, callback);
};

module.exports.insert = insert;
module.exports.update = update;

test.js

var sinon = require('sinon');
var expect = require('chai').expect;
var m = require('./client');
require('mocha');


describe('example', function () {
  var stub;
  beforeEach(function () {
    stub = sinon.stub(m, 'insert', function (data, callback) {
      console.log("override called");
      callback();
    });
  });
  
  afterEach(function () {
    m.insert.restore();
  });
  
  it('should call insert when m.update is called', function (done) {
    m.update({ status: 'ok' }, function () {
      sinon.assert.called(stub);
      done();
    });
  });
  
});