While the mutant enderman is dying, you can actually collect endersoul fragments by right-clicking them before they explode. Right-click again while sneaking if you want to drop an endersoul fragment.
Now with some endersoul fragments following you, all you have to do is drop (not right-click) an eye of ender.
The combination of the endersoul fragments and the eye of ender transform into your very own endersoul hand with 60 uses for each fragment originally following you. The endersoul hand deals 3 hearts as a melee attack, and has 240 maximum uses. It provides you with two abilities:
- Right-click blocks to pick them up and right-click again to throw them far away (or at mobs).
- Right-click while sneaking to teleport to any block within a radius of 128 blocks, as well as hitting nearby mobs from the impact (However, this ability damages the hand by four uses instead of one use).
Also, if your endersoul hand is running out of uses and you have some spare endersoul fragments, just toss out your endersoul hand while the fragments are following you and it'll recharge the hand again (with 60 uses each fragment).