Database

[{rootName:"AAA",outerItem:{innerItems:[{name:"A"},{name:null},{name:"C"}]}},{rootName:"AAA",outerItem:{innerItems:{name:"A"}}}]

Query

db.collection.update({},[{"$set":{"outerItem.innerItems":{$concatArrays:[{$slice:["$outerItem.innerItems",0,1]}]}}}],{"multi":true,"upsert":false})

Result