Last I used YourKit (v7.5.11, which is pretty old, current version is 12) it had two CPU profiling settings: sampling and tracing, the latter being much faster and less accurate. Since tracing is supposed to be more accurate I used it myself and also observed huge slowdown, in spite of the statement that the slowdown were "average". Yet it was far less than your results: from 2 seconds to 10 minutes. My code is a fragment of a calculation engine, virtually no IO, no waits on whatever, just reading a input, calculating and output the result into the console - so the whole slowdown comes from the profiler, no external influences.
Back to your question: the option mentioned - samping vs tracing, will affect the performance, so you may try sampling.
Now that I think of it: YourKit can be setup such that it does things automatically, like making snapshots periodically or on low memory, profiling memory usage, object allocations, each of this measures will make profiling slowlier. Perhaps you should make an online session instead of script controlled, to see what it really does.