To delete music off of your device, select and album and look for the multi-select icon on the app bar. Select it, and a series of checkboxes will appear next to the songs. Then, you can simply choose which songs you want to remove one-by-one – or tap the ellipses and choose “select all” to speed up the process – and hit delete. This works for songs stored locally on your device, as well as content in the Xbox Music Cloud.
Additionally, you can use this technique to download streaming songs to your device or add tracks to now playing.
While this isn’t necessarily the most intuitive way to delete content, it certainly makes the process of doing so faster and more granular. Which method do you prefer?