TimeSeries provides a fairly direct approach to this:
data = Import["https://pastebin.com/raw/QCAKwZ2P", "Package"];
dat1 = Select[data, 60 <= First[#] <= 140 &];
dat2 = Select[data, 10 <= First[#] <= 65 &];
ts2 = TimeSeries[dat2] ~TimeSeriesRescale~ {60, 140};
dat3 = {#, #2 - ts2[#]} & @@@ dat1;
ListPlot[{dat1, dat2, dat3}]
See also TimeSeriesResample.
Addendum
If I follow what you're asking for in the comments, try this:
ts2raw = TimeSeries[dat2];
datX = Array[{#, ts2raw@#} &, Length @ dat1, MinMax[First /@ dat2]];
Closely related but allowing for nonuniform sampling:
{t1, t2} = {dat1, dat2}[[All, All, 1]];
{m1, m2} = MinMax /@ {t1, t2};
ts2 = TimeSeries[dat2];
datY = {#, ts2@#} & /@ Rescale[t1, m1, m2];
Or:
{ts1, ts2} = TimeSeries /@ {dat1, dat2};
times = TimeSeriesRescale[ts1, MinMax @ ts2["Times"]]["Times"];
tsX = TimeSeriesResample[ts2, {times}]