Thanks to Eri for clarification on how to say "mowing the lawn" in Japanese. Another way of saying this in English is "cutting the grass". I think the phrase used depends on how serious a gardener one is. For instance, my father-in-law definitely "mows the lawn". He is English and has true English lawn to mow. He even manages to make those fancy mown stripes in his lawn.

On the other hand, I have a rather ratty American lawn, full of weeds and bare patches. So I'm just "cutting the grass".

I knew the Japanese word for grass was 草（くさ）. But I wanted to give the impression of an American suburban lawn which Martin's Pocket Dictionary includes as a synonym for grass しばふ. Takahashi's Pocket Dictionary concurs and gives the kanji 芝生.

Martin's does define mow as かります, but I missed it and Takahashi's does not. So I gave up on mow the lawn and tried for cut the grass.

If I had followed up on かる in Shogakukan's Bright Japanese-English Dictionary, I would have found it meant "cut, trim, clip, shear (sheep), mow, and reap. Ah, here is the sample sentence I was looking for...
[彼は日曜日に芝を刈った。」

I would then edit it to say...
私は土曜日に芝生を刈りました。

Now I notice that in the sample sentence しばふ isn't shown as 芝生, but as 芝. Why? I don't know. So I look しばふ up in the same dictionary and it shows 芝生.

Yes. I'm confused.