I was looking for if anyone had reported the problem, but I found nothing similar. So then I reported it :/
Trees dosen't drop items in survival mode in the normal difficulty with mobs.
Note also that I used an iPhone 5 with iOS 8.4 and Version 0.1.11 Alpha of Minecraft PE
Confirmed on iPhone 5 with iOS 8.4 and version 0.11.1 alpha of MC PE
2015-07-11, 11:09:12 PM UTC
2015-07-12, 10:25:54 AM UTC
ZiyenOfficial ZiyenOfficial 
MCPE-9212
I was looking for if anyone had reported the problem, but I found nothing similar. So then I reported it :/
Trees dosen't drop items in survival mode in the normal difficulty with mobs.
Note also that I used an iPhone 5 with iOS 8.4 and Version 0.1.11 Alpha of Minecraft PE
Confirmed on iPhone 5 with iOS 8.4 and version 0.11.1 alpha of MC PE