Unfortunately it seems that there isn't any "standard" way to reset the dictionary in Windows 10 Mobile. Hopefully this will be added back in soon. I don't want to try this for fear it will actually work, but you could try adding a different keyboard, removing your default one, then reinstalling it.
UPDATE: A post recently published by Microsoft states that you can reset your dictionary by going to Settings > Privacy > Speech, Inking and Typing and select "Stop getting to know me", "Turn off", "Start getting to know me", "Turn on."
EDIT: As of 10/13/2016, build 14946 (Fast Ring), Microsoft states that you can now remove custom words:
Option to remove a word from user dictionary (Mobile): We learn from your typing on the phone and build up a local user dictionary that adapts the keyboard prediction, autocorrection and shape writing experiences to your language style. Sometimes you may type a misspelled word and send it as is, sometimes you may tap on a red squiggled word and then tap the “+” sign by accident. Both save the unwanted word into your user dictionary, and it may appear when you type something similar in the future. Now you have a way to manually remove bad entries: tap on the word you don’t like in the text box, and you will see a candidate that is the word with a “-“ sign before it. Tapping on that candidate will remove the word completely from your user dictionary and no longer suggest it.
You may have to do the process twice, once capitalized and once lowercase.