I do this also. I was taught to sew a large seam with selvedges attached, then cut off the selvedges.

I also rip large pieces, then press the ripped edges and trim straight.

I'm a ripper for large pieces as well. Particularly with backing - if you know how it needs to be cut/ripped (that's always my challenge). I've not found extended damage when ripping. I press the edges and then trim as another poster mentioned. I've never had an instance of the fabric being damaged beyond the initial tear which always works out after ironing/pressing.

If ripping is not for you, I would suggest finding at least close to center of the length of your fabric and fold selvage to selvage. If you see a 'bubble' at the folded edge, wiggle the selvage edges until the bubble disappears. Pin to hold that position. I then lay that section on my cutting table and smooth out to the far edges from there. Eventually the selvage edges with 'wander' and you will have uneven edges but your fabric should be very close to on-grain at that point. Trim edges and go from there.

I rip my fabric for borders and backs. It's easier and faster than cutting large pieces.

Since I buy some fabric in multi yard cuts, I also will rip from selvage to selvage (across the grain) when I need a piece and don't want to unfold the whole thing But want to make sure I get a nice straight piece.

I fold large pieces down to a manageable size. I lay a square ruler on the fold, snuggle my 24" long ruler up to the square and cut. Hard to explain but, I learned this out of a Lynette Jensen quilt book. I am sure youtube will have how to square up fabric or google it.

I'm a folder also. As long as your ruler is perfectly perpendicular to your folds, your cuts will be straight and you won't have any V's.

Jingle, I much prefer your method. I've found that the threads in the fabric do not always run straight -- I've had some disastrously skewed "rips", so I just don't rely on ripping any more.

I've never had a problem with ripping but I have with cutting large pieces so I guess I'm a ripper. I do press the edges after ripping though.

I do this too. I fold the length (in your case 4 yds) in half so it is now 2 yds. long, and cut on the fold you just created. Open up and sew the selvages together along one side.

Thanks for the replies to my question. I took a deep breath and ripped my fabric, giving myself two smaller, more manageable pieces. Worked well. I'll do that again.