them ain't scraps.......them are PROFITS!
anything smaller than about 4" x 6" i toss with a tear in my eye - it's really hard to cut width's narrower than 4". anything of useful size i keep - if it's big enough i roll it and stick it back inside the tube with the 'mother' roll or if it's smaller, it's in a plastic shoe box that i keep next to my supply of rolls. i can't even count the number of names, single numbers or elements of left chest logos that i've cut from that 'drop' box - essentially material that's already been paid for by another job. if i've cut a 13" graphic from a 20" roll.....the original customer gets charged 20" x the length theirs required.
oh! do you mean adhesive sign vinyl? sorry, i thought you were talking heat press vinyl - it's monday again, isn't it

but.....same story - if it's a useable piece in a common color, i keep it - same storage method, except the 'drop box' is somewhat larger LOL
i just finished cutting logos for 30 bulletin boards for a large business client - every one of them out of the 'drop'
