Tying into clay sewer line

Is there a best way to cut into a clay pipe or just bust it out and put the rubber boots in so I can install a clean-out? Is there a standard size clay pipe used from the house to the main? I have dug down to the clay pipe (3.5'), but haven't determined the actual size.The pipe is in about 3' sections and is leaking at both end couplings. The leaking water is not black, it is a dirty brown, nor does it have a terrible, terrible smell. I'm also having trouble figuring out why water is running out of the pipe even when there is no water running in the house. I am having to put a sump pump in the whole to keep up with water pouring out of the pipe.

Have a plumber take a looksey at what you're talking about here. Couldn't hurt, could it¿

pipe

It should be 4" clay and the water is coming out because it is either plugged, or it is installed with backwards slope. you cut it with a snap pipe cutter.

clay pipe

Thanks for the info. I'm not familiar with snap pipe cutter, but I'm sure I could bye or rent one. Do you supose a guy could take a chizzle and hammer and bust that clay and couple it with a boot to pvs and install a clean-out. Thanks again.

Sorry to say but you have bigger problems if there is water in the pipe.
It's either clogged or bellied.

This is a soil pipe cutter AKA Snapper.
It will easily cut Cast Iron or Vitrified Clay Pipe.