A possible method in order to subdue a turtle would be to plop certain items onto the block that the turtle is stashing or hiding itself on. The items you can leave on the block matter as well, seeing as leaving sugar canes or melon slices should do the trick.
However, another way would be to breed the turtles so that you can acquire turtle eggs. This can be done by supplying two turtles sea grass. This will allow the turtles to enter a state known as love mode.
Then in a fit of Minecraft mother nature glory, one of the turtles will have the eggs in its inventory. The turtle with the eggs will increase in size. Since turtles are very particle on their beaches and birth places, the swollen turtle will return to lay the eggs on the same block it saw life.
The turtle will lay around 1-4 eggs. Moreover, it can have even more eggs promptly after having that batch of eggs.