Telford man Callum Williams, 25, said to his aunt he would "blow up her car and the house while she was inside" in a phone call on November 10 last year, a court heard.
The next day he also used a racial slur in a tirade at a man that had been his friend, Hakeem Smith.
Telford Magistrates Court heard on Wednesday from prosecutor Mr James Morris that Williams also breached a restraining order forbidding him from visiting his grandfather Malcolm's home in Wellington.
When arrested and interviewed by police he made "full and frank admissions" and said that he had been helping to look after his grandfather, Mr Morris said.
Mr Morris relayed the account of Hakeem Smith, who had been the target of a racist slur by Williams.
"He states the incident left him very anxious and his mental health has declined since the incident."
Acting for Williams, Mr Martin McNamara said that Williams was "exceptionally vulnerable" and had been supported by his aunts and his grandfather throughout the period despite the restraining order.
He lives with ADHD and autism, the court heard.
Williams, of Hayward Avenue in Donnington, pleaded guilty to sending an offensive/indecent/obscene/menacing message and racially aggravated harassment without violence.
He also pleaded guilty to four offences of breaching a restraining order.
Chair of the magistrates bench Mr Alan Parkhurst told Williams: "The incidents themselves were distressing for your family who had done their best to support you.
"Mr Smith was, in his own way, trying to help you too.
"[The period] was disturbing for everyone involved and you don't want it to happen again."
He handed down a community order with the requirement that Williams carry out 60 rehabilitation activity days.
He must also pay a fine of £80 and a £95 victim surcharge. Mr Parkhurst told Williams to "reflect on the upset caused" and try to resolve his anger issues.
The prosecutors did not seek a new restraining order against Williams.