He will if he is, under proper legal authority, ordered to.
Mueller does not really want to testify. The reason the democrats want his testimony is because they want to be able to act on his statements. They want him to say "I believe there was collusion" or "I believe there was obstruction." In this way, they can say the head of the special council recommended investigation or impeachment hearings.
If, however, the democrats are left to read his report(s) and make their own calls, they own that decision. AOC, for example, can say whatever the fuck she wants - she hasn't been there to review classified material multiple times, nor was she making various deals in closed rooms. If she drums for impeachment, no one can come back and say that she knew that what is redacted in the SC's report and various related documents vindicates POTUS.
On the other hand… If those who know the truth about spygate push for impeachment… then they are walking a very dangerous line as the senate hearing will clear those redactions.
Thing is - Mueller already had the opportunity to say those simple words. By wording his response as he did, he left it open for the Democrats to charge through that line.