Manager David Holdsworth told BBC Radio Nottingham: "He's a tough guy, he will add another bit of quality.
"He can play left-back, so he's a versatile defender. He won't accept second best and he likes putting his head in where it hurts."
Grand said: "It's come from me not being able to break into the team at Fleetwood.
"So, when the opportunity arose to come and get some games at such a good club, I couldn't afford to turn it down."
Former Stags defender Day, 28, has struggled this season with a knee injury and is yet to feature for the U's in League Two.
Oxford manager Chris Wilder told BBC Radio Oxford: "It's good for him and good for Mansfield.
"They're getting a really decent player, who's won the league with Aldershot and got promoted with us, so I wish him all the best."
Source: BBC Sport