Demo song: http://remixta.net/stuff/stretchgate.xrns
How I made it.
First pattern
Plays regular amen break. The 2F00 effect on the top turns OFF the gainer device in track DSP, will talk about that later. To create those effect on/off effects place your edit cursor on the line where you want it entered and RIGHT click on the effect toggle checkbox.
Second pattern
The break is timestreched with 09XX command.
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Enter the note on every line and also place the 0900 command to it’s side. (Easiest way of doing this is that you create one row with C-4 0900, select the row, press CTRL-C to copy and CTRL-P to continuous paste, but you may just hold down right keys and pan through the whole pattern).
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Edit the the effect on last row to something like F5 or so (the right value may depend, just try what sounds best for you).
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Press Shift - I (Interpolate track). It interpolates the values (fills in missing values) between the first row and last row.
09XX is “sample offset” command, what actually happens is that the effect places playback in sample to positions described in the effect, in this example it constantly “rewinds” the sample on every long to make it sound longer.
There is also Alt-I that interpolates the selected block instead of the whole track, also all those effect interpolation functions are available in right click menu.
Third pattern
Gating with pattern effect command. The 04XY command slices currently playing row, so you need to cover all the area that you want to hear the slicing on. As you can see I covered the whole track.
The first parameter gives the volume when slicer is closed 0 means silence I used 2 for bit softer result.
Second parameter is when the slicer kicks in on a row. Smaller number means more silence, higher number means less silence.
Fourth pattern
Gating with LFO and gainer device. That gives similar result to previous pattern, just that you have more control how the sound is formed. Check the DSP chain window how the LFO device and gainer devices are set up.
Fifth pattern
I realized just now that you want beatslicer. So I made this pattern.
The amazing 09XX effect comes into play again. Instead of cutting one sample into smaller pieces you can choose where the sample is started, giving you full control over rearranging loops.
The numbers in 09XX are taken from sample editor bottom ruler. Just see which places in sample seem interesting for you and write down or memorize those numbers. Then use them together with 09XX effect. Really useful stuff as you can see. 
You can read more about pattern effect commands here: http://tutorials.renoise.com/Renoise/EffectCommands