The word 'safe' is relative. some parts of the Dominican Republic are unsafe for example like the capital Santo Domingo are unsafe. Punta Cana is very safe to get around but of course, you should always use common sense, don't invite trouble, be aware of your surroundings, etc. Dominicans are friendly, welcoming, helpful people, but there is poverty that drives crime, like anywhere. One thing is for sure Punta Cana is no less safer than some parts of NY or NJ. Any good Dominican will  tell you to be smart in the street at night or in desolate areas, but I think the common criminal avoids foreigners fearing more punishment

  HERE ARE  FEW THINGS TO KEEP IN MIND 

• Do not over expose your valuables (Cell phones, jewerly, cameras, fancy devices, etc)
• Carry minimum amount of cash. (Credit Cards are widely accepted in DR).
• If taking a cab, go for those with a registered union. (look for uniforms on the drivers, signs or stickers on their cars.
• Do not take yourself to isolated, remote areas out of your resort. Stay with the crowd.
• Keep your Id’s separate from cash in your pockets.
• Strangers approaching you out on the streets, to offer you goods or services may rip you off, so evaluate your options (shop around).
• Use good judgment, before making a decision out there. Stay safe.