Having a beehive in your garden can be very troublesome because it is dangerous especially if you are allergic to them.
However you can remove the beehive but you will have to be very careful how you go about getting rid of the hive; this procedure can be done by simply getting yourself a bee suit and a good insecticide. When you use an insecticide then this will freeze the bees and you can get rid of the bees like that however if this is not an option for you then you could start a fire in the hive to do so.
For your first step you are going to need to rent the smoker and get everything that you need for removing a beehive safely. Most of these things are going to be able to get from a home improvement store so you need a fire hose a smoker which might be a little difficult to find but an insecticide for your bees and of course your bee suit which should also have a hood is required.It might be better if you rent a smoker which you are going to need later so that you can get cleared of the beehive later; there hopefully will be one or two stores around that lets you rent a smoker. This will start a small fire and acts as your diversion to get the bees to there so you can work safely on the hive.For the smoker you are going to need to use this to start your fire, this smoker will let you do this safely so that you can get near the hive. The smoker is a calming method for the bees and that way you are going to be able to apply your insecticide to the inside of the hive.
Put your bee suit on and then you can get near to the hive but make sure you go very slowly to the hive because you need to put the smoker right underneath the hive because the bees will be deflected to the smoke which allows you the time to spray your solution into the hive. All the bees go to the smoke as you put the end of the applicator into the beehive and spray into the hive This is an insecticide but if this is not what you want to use then use a fire to destroy the actual hive but remember to have a hose nearby so that if it gets out of control then you can put the fire out.Now you can go ahead and take down the nest from your tree and then you should dispose of the hive safely and not to just leave it lying around your garden or anywhere unsafe.