Depending on the depth and breadth of your specific requirements, JMP has many of the building blocks that you might need. For example, the following code generates some random data and shows how to fit two Gaussians (using 'Analyse > Distribution'). Do 'File > New > New Script', copy and paste the code into the window that appears, then do 'Edit > Run Script'):
NamesDefaultToHere(1);
// Make some data with two peaks . . .
n1 = 500; mu1 = 0; sig1 = 1;
n2 = 500; mu2 = 2; sig2 = 2;
peak1 = J(n1, 1, RandomNormal(mu1, sig1));
peak2 = J(n2, 1, RandomNormal(mu2, sig2));
peaks = VConcat(peak1, peak2);
dt = NewTable("Peaks", NewColumn("Y", Numeric, Continuous, Values(peaks)));
// Use 'Normal Mixtures' in 'Distribution' to fit
dt << Distribution(Continuous Distribution( Column( :Y ), Fit Distribution( Normal Mixtures( Clusters( 2 ) ) )));
But you probably want to fit a mixture of Lorentzians, in which case you will need 'Analyse > Modeling > Nonlinear' (see, for example: https://www.jmp.com/about/events/summit2013/resources/Paper_Susan_Walsh.pdf to get started with this).
However, remember that JMP is 'all purpose' statistical software: If you want the full range of capabilities that more niche software provides for dealing with spectral data, you would have some work to do, and require some knowledge to do it.