MCT refers to connections on a single ticket. Below the MCT and the airline may not ticket, or offer any protection in the event of misconnect (in practice airlines generally do help pax who misconnect, especially if fare is premium cabin or pax is elite).

With separate tickets, the MCT comes into play for checking bags through. With a connection under MCT there is a risk that airline will not check bags through. However the main consideration with separate tickets is getting checked in before the onward flight closes for check in (30 minutes for SQ at SIN).

A 60 minute connection SQ->SQ at SIN will in normal circumstances be enough to beat the check in deadline - I have done this before and so far made it each time. However, if your first flight is more than 20 minutes late then you may miss your connection (this assumes no checked bags or if you have any they are checked through to final destination). Up to you how comfortable you are with this risk - a status pax on a premium cabin ticket to a destination with lots of flights and I'd be relaxed, a non-status pax flying economy to a destination that only has a few flights a week and I'd be inclined to allow more time (on separate tickets).