Mix sauerkraut, beer or cider, and mustard in small skillet and simmer 10 minutes.
Cut kielbasa into 4 portions and split sausage pieces in half, opening them up.
Grill the sausages on hot griddle until crispy on both sides, about 7-8 minutes total.
Wipe some of the grease off the griddle and drop heat to low.
Lightly butter 1 side of each slice of bread. Build butter-side out sandwiches out of grilled kielbasa, sauerkraut, and 2 slices of cheese; spread the top of each sandwich with red pepper relish before setting in place.