You can utilize the custom deployment script feature where you add a step that cleans up the packages
directory.
You can read about it here: http://blog.amitapple.com/post/38418009331/azurewebsitecustomdeploymentpart2/
Another option is to add a post deployment action, by adding a script file (.cmd/.bat) that has the clenup logic to the following directory in your site: d:\home\site\deployments\tools\PostDeploymentActions\
, this script will run after the deployment completes successfully.
Read more about it here: https://github.com/projectkudu/kudu/wiki/Post-Deployment-Action-Hooks