I saw a dog running around in circles chasing his tail.
I saw a dog going round and round trying to bite his tail.
この場合、次のような言い方ができますよ。
ーI saw a dog running around in circles chasing his tail.
「犬がしっぽを追いかけて回っているのを見た」
to run around in circles で「ぐるぐる同じところを走り回る」
to chase one's tail で「しっぽを追いかける」
ーI saw a dog going round and round trying to bite his tail.
「犬がしっぽを噛もうとぐるぐる回っているのを見た」
to go round and round で「ぐるぐる回る」
to bite one's tail で「しっぽを噛む」
ご参考まで！
カナダ 
