williamreinecke

Is there a way to stop the brake fluid from leaking out while a caliper is removed or changing the slave cylinder?

Rushjob

Use a brake pipe clamp on the flexi or place cling film over the fluid reservoir are two pretty basic methods.
How old is your brake fluid?
It may well be worth changing it anyway.

JasonAndreas

Before you crack open a brake line you should pump the brake pedal (with the car turned off) 20-30 times (to relieve pressure) and then put something (a piece of wood, etc.) wedged between the seat and the pedal so that the pedal is pushed halfway down. That will stop brake fluid from leaking out. Residual fluid left in the caliper can still come out but nothing will from the lines. When I sent my calipers out for powder coating a few years ago it took nearly 3 weeks to get everything back and I only had a few drops of brake fluid leak out. The same should apply to the clutch slave cylinder (I didn't think of it when I swapped my CSC but it wasn't too messy). Just remember that once the new slave cylinder is attached to the line that you don't want to re-push the clutch pedal down unless the cylinder is also attached to the clutch release fork or you will push out the piston dust boot. If you do manage to push out the dust boot you can reattach it but it is a PITA.

williamreinecke

I used the cling wrap and had almost no leaks. Replacing the slave was a PITA. And it did not solve the problem. I guess a clutch is in my future.

ThomasC2

William, it could also be the front clutch/master cylinder (under the pedal). Not all problems are because of the slavecylinder in the rear even if it's most common.