Only when Don McGahn, the White House counsel, refused to carry out the order, arguing that it would have a catastrophic effect on the presidency, did Trump back down.
Ironically, the fact that Trump tried to remove Mueller only makes the latter's case stronger that the President attempted to obstruct justice by trying to derail the criminal probe into his and his associates' activities. Many legal experts argue that Mueller already has a strong case for obstruction based on the firing of former FBI Director James Comey and Trump's statements and actions thereafter. This latest news only makes the case worse for Trump.
This is definitely a developing story and more is likely to shake down this weekend and next week. Definitely stay tuned.