Database
[{"_id":"xxxxxxxxxxxxxxxxxxxxxxxx","Name":"HelloWorld","OtherFields":"OtherValues","Projects":[{"Project":{"key":111},"Category":[{"No":"123"},{"No":"987"}]},{"Project":{"key":222},"Category":[{"No":"123"},{"No":"987"}]}]}]
Query
db.collection.update({"_id":"xxxxxxxxxxxxxxxxxxxxxxxx"},{"$pull":{"Projects":{"$and":[{"Project.key":111},{"Category.No":"123"}]}}})