I suppose he could, but history has show us it isn't a good idea. Nixon fired Archibald Cox in the "Saturday Night Massacre," and this led to Nixon resigning to stave off impeachment. Trump surrogates--Sean Hannity, Rush Limbaugh, Mark Levin, and Newt Gingrich--are urging firing Mueller. This isn't a good group to seek advice from, but Trump does get his news from Fox. So what do you expect? Regardless, he is getting horrible advice.
If Trump fires Mueller, it will be strong evidence of obstruction of justice and likely result in a deeper probe. Ultimately, Trump will likely be out of office before the end of his first term. I don't see him withstanding all of this.