Place all marinade ingredients in a food processor and blend until a smooth paste. Combine with chicken and beef pieces (in separate bowls) and leave to marinate in the fridge for at least 1 hour or up to overnight.
Thread marinated beef and chicken onto bamboo skewers and set aside until ready to cook.
To make the peanut sauce, combine lemongrass, ginger, cumin, coriander and chili paste in a food processor and blend until smooth. Heat oil in a wok and fry the spice paste for a few minutes until fragrant. Add ground peanuts, water, tamarind juice, and sugar. Season with salt and simmer until thick, about 5 minutes.
Cook beef and chicken satay on a preheated barbeque or grill plate until cooked through, about 3 minutes each side.
Serve satay with peanut sauce, cucumber and red onion.