When a person has said many things over the course of their life, those statements may not always be perfectly consonant with one another. Using the definite article the is an acknowledgement of that dissonance or lack of agreement between one statement and another:
Where's the President Trump who promised a middle-class tax break?
It's as if to say there is more than one version of the person, and the speaker is singling out one of them.
P.S. In the specific context of Jesus, he is known only via the biographical traditions that present his life and sayings, and thus there are literally "versions" of Jesus. Sometimes, as Jeff says, the speaker who uses that phrase is promoting the version that they consider the "true" version; at other times it is simply a recognition of there being multiple versions to choose from. I don't think it's possible to say from that brief interview which meaning the bishop has in mind.
P.P.S. In the context of the utterance in the video, the restrictive clause "who said 'Blessed are ...'" is part of the specification and essential to the distinguishing of this Jesus from some other Jesus (or Jesuses) who did not say those words. And that need not be taken literally to mean that multiple historical persons named Jesus are being distinguished from one another; it can be simply a manner of speaking, a figurative use of the definite article, just as grandpa can say to Billy who won't eat his Wheaties:
Where's the Billy whose favorite cereal is Wheaties?
What you make of the statement from that point on (whether it is a comment critical of people who don't really understand the "real" Jesus, or a reference to the fact of there being multiple views of Jesus in the lives that have survived as gospel or multiple views that have resulted from different interpretations thereof) is a matter of cultural interpretation, not of English grammar.