Cancellation of 1 flight on multi-city booking. Am I entitled to a full refund?

If I'm reading Singapore Airlines' contract of carriage, the airline will offer you a delayed itinerary, a re-routing, or a refund; and the change must be done "with the agreement of the passenger." If you end up getting a refund, you're entitled to get back a refund for "the unused portion of the ticket"; and if you haven't already taken any of the flights in question, then the "unused portion" is the entirety of it.

It is possible that Singapore Airlines' conditions of carriage are superseded by Air New Zealand's equivalent document in this case. My impression is that Singapore Airlines' conditions still apply to aspects of the fare, refunds, etc.; but I am not 100% sure on this.

That said, even in normal times, the airline would prefer not to give you a refund, and will offer you other options that don't involve giving you your money back, such as re-routing or vouchers. With the COVID crisis, this goes double; airlines are trying to hold on to every bit of revenue they can right now. Expect a "hard sell" if you ask for a refund.

Relevant text of the conditions of carriage are below.

Art. 10 Para. 2. Cancellation, Changes of Schedule, etc.

(a) If Carrier cancels, terminates, diverts or fails to operate a flight reasonably according to schedule, is unable to provide previously confirmed space, fails to stop at a Passenger’s stopover or destination point, or causes the Passenger to miss a connecting flight on which he holds a reservation, Carrier may, subject to the requirements of applicable laws and regulations, elect one of the following options, with the agreement of the Passenger, either:

(1) carry the Passenger as soon as it can on its scheduled service; or

(2) re-route the Passenger to the destination indicated on the Ticket or applicable portion thereof by its own scheduled services or the scheduled services of another carrier, or by means of surface transportation. If the sum of the Fare, excess baggage charge and any applicable service charge for the revised routing is higher than the refund value of the Ticket or applicable portion thereof, Carrier shall require no additional Fare or charge from the Passenger, and shall refund the difference if the Fare and charges for the revised routing are lower; or

(3) make a refund in accordance with the provisions of Article 11 Paragraph 3.

Art. 11 Para. 3. Involuntary Refunds.

If Carrier refuses carriage in accordance with Article 3 Paragraph 3, Article 8 Paragraph 1 (subject to Article 8 Paragraph 2) or in accordance with Article 9 Paragraph 3, or in any of the events set out in Article 10 Paragraph 2, then subject to Article 11 Paragraph 1, the amount of the refund shall be calculated in respect of the unused portion of the Ticket. Carrier’s Regulations provide information as to how the refund payable will be calculated.