I think you should remove - from command -60 min ago so only it will give time and date before 60 mins else it is giving 60 mins after time(you could take it as a maths concept of -ve * -ve = +ve kind of). Because you are already using keyword ago and then you are mentioning value -60 mins ago , so it will print value after 60 mins.
Here is what is the difference between -60 mins ago and 60 mins ago.
Current time:
date +'%Y-%m-%d %H:%M:%S,%3N'
2016-08-24 04:38:14,141
Using -60 mins ago :
date --date '-60 min ago' +'%Y-%m-%d %H:%M:%S,%3N'
2016-08-24 05:38:31,415
Using only 60 mins ago :
date --date '60 min ago' +'%Y-%m-%d %H:%M:%S,%3N'
2016-08-24 03:38:34,060
Now for taking values from a variable following may help you in same.
var=60 ##You could assign any value as per your need here.
date --date ''"$var"' min ago' +'%Y-%m-%d %H:%M:%S,%3N'