Send a Google Doc in an email using Apps Script

SendDocument.js

/**
 * Sends an email using the contents of a Google Document as the body.
 */
function sendDocument(documentId, recipient, subject) {
  var html = convertToHtml(documentId);
  html = inlineCss(html);
  GmailApp.sendEmail(recipient, subject, null, {
    htmlBody: html
  });
}

/**
 * Converts a file to HTML. The Advanced Drive service must be enabled to use
 * this function.
 */
function convertToHtml(fileId) {
  var file = Drive.Files.get(fileId);
  var htmlExportLink = file.exportLinks['text/html'];
  if (!htmlExportLink) {
    throw 'File cannot be converted to HTML.';
  }
  var oAuthToken = ScriptApp.getOAuthToken();
  var response = UrlFetchApp.fetch(htmlExportLink, {
    headers:{
      'Authorization': 'Bearer ' + oAuthToken
    },
    muteHttpExceptions: true
  });
  if (!response.getResponseCode() == 200) {
    throw 'Error converting to HTML: ' + response.getContentText();
  }
  return response.getContentText();
}

/**
 * Inlines CSS within an HTML file using the MailChimp API. To use the API you must
 * register for an account and then copy your API key into the script property
 * "mailchimp.apikey". See here for information on how to find your API key:
 * http://kb.mailchimp.com/article/where-can-i-find-my-api-key/.
 */
function inlineCss(html) {
  var apikey = CacheService.getPublicCache().get('mailchimp.apikey');
  if (!apikey) {
    apikey = PropertiesService.getScriptProperties().getProperty('mailchimp.apikey');
    CacheService.getPublicCache().put('mailchimp.apikey', apikey);
  }
  var datacenter = apikey.split('-')[1];
  var url = Utilities.formatString('https://%s.api.mailchimp.com/2.0/helper/inline-css', datacenter);
  var response = UrlFetchApp.fetch(url, {
    method: 'post',
    payload: {
      apikey: apikey,
      html: html,
      strip_css: true
    }
  });
  var output = JSON.parse(response.getContentText());
  if (!response.getResponseCode() == 200) {
    throw 'Error inlining CSS: ' + output['error'];
  }
  return output['html'];
}

This still works for me, it is not deprecated. You just need to make sure you enable the Drive API under services.