"When we are busy, it's a bad thing for the world," he says, looking out over central London from the society's high-rise office.
"The past four months have been extraordinary because we've seen such a confluence of events. They are all linked. Every crisis in the world is caused by an authoritarian, dictatorial regime."
The Israeli-Palestinian conflict is one of the society's main focuses, and Dr Mendoza's team has worked hard to convey the importance of the IDF's Operation Protective Edge within the multitude of problems facing the international community.
"To us it became quite obvious there was linkage between hatred of what we stand for here in this country and in America, and also hate of Israel," he explains.
"We are not a Jewish organisation but our view is: 'Israel is a democratic ally in the world and in a tough region'.
"I think it's very dangerous to assume that most people are anti-Israel or anti-American. Our experience has been that actually most people don't have a set view on any of those issues."
The fallout from the Gaza conflict has led to rising antisemitism in Britain, but while tensions run high in the Jewish community, Dr Mendoza said despair should not be the only option.
"There's a sense that everyone is against the Jewish community and it has no friends, but we can show you lots of cases of people who have been supportive, lots of people who understand the core argument that this isn't about Israel or the Jewish community. It's a question for all of us who stand against the rising tide of radical Islam.
"It's about being open to the fact there are friends out there. One of the advantages of not being a Jewish organisation is that we don't have that bunker mentality. We can provide that sword to complement the shield that other organisations provide so well. You need both if you're going to succeed."
Dr Mendoza's organisation may not be Jewish but he himself is firmly rooted in the community.
He was a pupil at North West London Jewish Day School before studying at Cambridge (where he also wrote his doctoral thesis on on Anglo-American relations during the Bosnian War) and is now on the board of the Spanish and Portuguese Jews' Congregation. He is married to Claudia, who is head of policy and research at the Jewish Leadership Council.
He acknowledges that many of the society's representatives are outspoken, often controversial figures. HJS associate director Douglas Murray is one of the country's most forthright commentators on neo-conservatism and Islamism.
But Dr Mendoza argues that "unshackling" people with strong views and providing a platform for them is one of the most effective methods of challenging opponents.
"It's all very well being defensive but you need, sometimes, to take the fight to the enemy. We have consistently done that. We are not afraid. We will make points others will fear to make because we know that by doing so we put the other side on the back foot.
"I like the fact that the right kind of people hate our appearances. When you get the 'Guardianistas' and radical Islamists complaining about the HJS putting this point of view across, you know you're doing the right thing."
Named after a former United States senator who supported Israel and campaigned for Soviet Jewry, the society is a relative newcomer in its field.
Started just 10 years ago, in its infancy Dr Mendoza ran it as a website from his bedroom, unpaid.
The leading organisations of their kind - Chatham House and the Royal United Services Institute - date back to the 19th or early 20th centuries and have multi-million pound budgets.
HJS operates on a budget of around £1.2 million a year, which pays for a team of researchers who put out academic-style publications and run speaker events.
It also has a university off-shoot called Student Rights, which promotes tolerance on campus.
It is currently setting up a centre working specifically on researching terrorism and radicalisation. It will look at issues including dealing with jihadis returning to Britain from Iraq and Syria, and the availability of Islamist materials online.
Dr Mendoza said: "The idea is to influence policy and make a positive change in this country and beyond. What we try to do is bring a perspective that often isn't heard in the media, in the think tank community and politically and bring it to the fore."
With so many global flashpoints and such division within domestic politics on tackling the issues, does he not feel an air of desperation when going to work every day?
"Foreign policy is like a large tanker coasting along. You do something but the effect is only seen some time afterwards when the tanker turns," he says.
"Our challenge over the next year is to put some of the ideas we have been thinking about for a long time firmly onto the agenda of government and the political parties.
"One thing everyone who shares these values has to do is see the long game. We don't necessarily have to get a result tomorrow - it's about winning the long-term battle."
