Is there a way to set a max running time, or maximum number of cuts, when solving an integer problem with mosek? Or at least a way to stop a running optimization? It seems when the solver is running, the only way to stop it is shutting down matlab?
Stopping cvx (mosek)?
Mosek has lots of parameters, incl. time limits etc.:
https://docs.mosek.com/8.1/toolbox/parameters.html
And in the second FAQ question it shows how to set them from CVX:
@Michal_Adamaszek nicely answered your question about changing Mosek parameters prior to Mosek being called by CVX.
As for terminating Mosek while it is in the middle of solving a problem provided by CVX, it seems that ctrl-C is generally effective in quickly halting Mosek and returning control to the MATLAB command line, at least under Windows, and I suspect under other operating systems as well. I have to defer to someone else whether situations ever occur in which Mosek is in the middle of something and non-responsive to ctrl-C. There are some mex optimizers under MATLAB which are non-responsive to ctrl-C, for which killing the MATLAB session may be the only way of stopping execution.
He did indeed. I didn’t reply ‘thanks’ because apparently that’s too short a post for this forum. I did ‘like’ it though 
On my system (windows 10 with matlab 2016b), crtl-c does not stop mosek, at least not during my integer problem. I get something like this instead:
941 940 856 7 -8.0331941223e+003 -1.1848245370e+004 47.49 55.4
1064 1063 979 8 -8.0331941223e+003 -1.1837168401e+004 47.35 61.0
1186 1185 1097 11 -8.0331941223e+003 -1.1811499176e+004 47.03 66.6
1308 1307 1219 42 -8.0331941223e+003 -1.1811499176e+004 47.03 72.2
1431 1430 1320 8 -8.0331941223e+003 -1.1808082791e+004 46.99 77.7
1552 1551 1431 8 -8.0331941223e+003 -1.1806416583e+004 46.97 83.5
1672 1671 1541 26 -8.0331941223e+003 -1.1800970040e+004 46.90 89.0
Operation terminated by user during cvx_mosek
In cvx_mosek
In cvx_run_solver (line 50)
[ varargout{1:nargout} ] = sfunc( inputs{:} );
In cvx_mosek
In cvxprob/solve (line 429)
[ x, status, tprec, iters ] = shim.solve( At, b, c, cones, quiet, prec,
solv.settings, eargs{:} );
In cvx_end (line 88)
solve( prob );
1793 1792 1648 56 -8.0331941223e+003 -1.1800970040e+004 46.90 94.8
1914 1913 1763 11 -8.0331941223e+003 -1.1800970040e+004 46.90 101.7
(it acknowledges ctrl-c, but then continues)