Hello Jeff,
Based on my understanding, you would want to clone an existing ad group together with its keywords. If so, there is currently no way to copy an ad group. However, you may use the AdGroupBuilder to create a new ad group with configurations the same as the ad group you would want to copy. 
Here is an example script as reference on how to create ad groups.
Please take note that when creating the ad group, 
these are the only methods available. If you would want to add exact keywords on the ad group that you will be creating, you must first create the ad group. You may then use the 
KeywordBuilder to add exact match keywords. 
Here is an example script on how to ad keywords on an exiting add group. To add an exact match keyword, you may add brackets ([]) in the text inside the withText() function (e.g. 
withText('[SAMPLE]')).
You may also see the sample script below on how to create ad group and add exact match keyword on the said ad group as reference:
function main() {
  var campaignSelector = AdWordsApp
  .campaigns();
  var campaignIterator = campaignSelector.get();
  while (campaignIterator.hasNext()) {
    var campaign = campaignIterator.next();
    Logger.log(campaign.getName());
    var adGroupOperation = campaign.newAdGroupBuilder()
    .withName('INSERT_ADGROUP_NAME_HERE')
    .withCpc(INSERT_CPC_HERE)
    .build();
    
    var adgroup = adGroupOperation.getResult();
    if(adGroupOperation.isSuccessful()) {
      //creates the exact match keyword on an adgroup level
      //note that all adgroups on this specific campaign will have exact match keywords created
      var keywordOperation = adgroup.newKeywordBuilder()
      .withText('[INSERT_KEYWORD_NAME_HERE]')
      .withCpc(INSERT_CPC_HERE)
      .build();
      var keyword = keywordOperation.getResult();
    }
  }
}
To delete all keywords under an ad group, you may refer to the sample code below as reference:
Let me know if the suggestions above works for your requirements.