In an interview for BBC Radio 4's The Food Programme to be broadcast on Sunday, he points out that few people ever see elderly sheep and are surprised by their appearance.
"I live on a sheep farm so we shear the sheep, but they die of old age -- and you know what, it's kind of embarrassing, because none of the other farms have got old sheep," he said.
"They're all gone before they're old -- they just die like we do. It's life, it's death, it's what happens.
"We just give them a good life and I take the wool from them. But it can be embarrassing, you know, people say 'look at the state of your sheep' and I say 'yes they're very old' and you know there is only one alternative -- send them to the knacker's."
In an interview with presenter Sheila Dillon, Paul talks about his vegetarian lifestyle and his desire to encourage more people to try eating less meat.
It comes as his late wife Linda's veggie food range is given a new push, with a TV ad campaign and new products. McCartney is also publicising the idea of taking a break from animal products with "meat-free Mondays".
In the programme, to be broadcast tomorrow at 12.30pm, he explains: "Basically what we're saying with the meat-free Monday campaign is that out of your seven days, you might think of one day being meat-free.
"We're saying 'just try one day'."