Ok, I am now in the land of guesswork and speculation which is not the best
I cannot see Alexander and wife Mary in 1861, nor can I see a death for them post 1855 at this stage. On the hopeful side, Gadget here on RC has the MIs for Borgue so you could ask her to have a look to see whether she can find something on them for deaths perhaps.
Whilst searching for Mary's death, there was another one close that I have had a look at the image.
This Mary McMinn was single, died in 1869 aged 83. I saw her entry earlier in the 1861 showing as born in Twynholm. Parents Alexander McMinn, a mason, mother (blank) Sproat m.s.
Pure speculation part from me at this stage, I would mark her down as possible 'aunt' to our Alexander at this time. If our Alexander was first born to Alexander, mason, and wife Mary, then likely he would have been named after paternal grandfather. Perhaps also the male McMinns were a line of masons by trade. Supporting this (new!) theory, there is a John McMinn showing in 1851:
John McMinn 74, mason, b. Twynholm, Kirkcudbt
Irvine McMinn 67, wife, b. Kirkcudbright, Kirkcudbright
Margret McMinn 35, daughter, b. Borgue, Kirkcudbright
Address: Swin Drum, Borgue, Kirkcudbright
