We can analyze this sentence's structure as SVC (subject-verb-complement):
Subject: what he did
Complement: exceed our expectations and push performance art to a new level
The subject is a nominal clause. It is fairly straightforward, with the wh-word (which functions as the clause's direct object) fronted.
The complement (in this case a predicate nominative) is a series containing two conjunts connected by "and". Each conjunct is a nominal phrase headed by a bare infinitive (which I've put in bold). It is, indeed, somewhat unusual for a bare infinitive to head a nominal phrase, but it is correct. BillJ notes that this is possible because the nominal clause's main verb is "to do".
Here is an example of a similar construction from what I believe is a transcript of a House of Lords committee hearing ("House of Lords - Committee for Privileges and Conduct: The Conduct of Lord Laird - HL 96: 10th Report of Session 2013-14", pg. 211):
Subject: what you do
Complement: go outside and try to create the climate of opinion
By the way, this is sometimes called a "pseudo-cleft sentence". It is not the most typical kind of cleft sentence.