I'll take a wild guess that you want to remove username, email, and password entirely. If so, you're looking for delete, which removes properties from objects:
app.get('/users', function(req, res){ Users.find{}, function(err, usersArray){
  for(var a = 0; a < usersArray.length; a++){
    var userData = usersArray[a].userData;
    delete userData.username;
    delete userData.email;
    delete userData.password;
    ...
  }
  res.render('users.ejs', {
    // and the variables go here...
  })
}
If those propeties are non-configurable, delete can't remove them, and you have to make do with setting their values to undefined:
app.get('/users', function(req, res){ Users.find{}, function(err, usersArray){
  for(var a = 0; a < usersArray.length; a++){
    var userData = usersArray[a].userData;
    userData.username = undefined;
    userData.email = undefined;
    userData.password = undefined;
    ...
  }
  res.render('users.ejs', {
    // and the variables go here...
  })
}
If they're both non-configurable and non-writable, you'll have to create replacement objects instead.
Live Example using delete:
var usersArray = [{
  userData: {
    name: "User 1", // Something to have left after we remove the others
    username: "user1",
    email: "user1@example.com",
    password: "pa$$word"
  }
}, {
  userData: {
    name: "User 2",
    username: "user2",
    email: "user2@example.com",
    password: "pa$$word"
  }
}, {
  userData: {
    name: "User 3",
    username: "user3",
    email: "user3@example.com",
    password: "pa$$word"
  }
}];
snippet.log("Before: " + JSON.stringify(usersArray, null, 2));
for (var a = 0; a < usersArray.length; a++) {
  var userData = usersArray[a].userData;
  delete userData.username;
  delete userData.email;
  delete userData.password;
}
snippet.log("After: " + JSON.stringify(usersArray, null, 2));
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Live Example with non-configurable properties using undefined:
function makeUserData(name, username, email, password) {
  var ud = {name: name};
  Object.defineProperty(ud, "username", {
    enumerable: true,
    configurable: false,
    writable: true,
    value: username
  });
  Object.defineProperty(ud, "email", {
    enumerable: true,
    configurable: false,
    writable: true,
    value: email
  });
  Object.defineProperty(ud, "password", {
    enumerable: true,
    configurable: false,
    writable: true,
    value: password
  });
  return ud;
}
var usersArray = [{
  userData: makeUserData("User 1", "user1", "user1@example.com", "pa$$word")
},{
  userData: makeUserData("User 2", "user2", "user2@example.com", "pa$$word")
},{
  userData: makeUserData("User 3", "user3", "user3@example.com", "pa$$word")
}];
snippet.log("Before: " + JSON.stringify(usersArray, null, 2));
for (var a = 0; a < usersArray.length; a++) {
  var userData = usersArray[a].userData;
  delete userData.username;
  delete userData.email;
  delete userData.password;
}
snippet.log("After delete: " + JSON.stringify(usersArray, null, 2));
for (var a = 0; a < usersArray.length; a++) {
  var userData = usersArray[a].userData;
  userData.username = undefined;
  userData.email = undefined;
  userData.password = undefined;
}
snippet.log("After assigning undefined: " + JSON.stringify(usersArray, null, 2));
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