Understand that your process of grieving will be unique. Do not try to fall into conform ideas of grieving. Grief can have a variety of expressions and differ from person to person. You might feel anger, sadness, guilt, fear or something completely different.  
Turn to family and friends. Talk about what you are experiencing and the feelings you have. Talking to others can help you cope, and you might experience that others feel the same way. However, keep in mind that everyone's grieving process is different, so do not expect the same expressions of grief from your friends and family.
Express your feelings in a creative way. If you have trouble expressing your feelings, you want an outlet or a way to name your feelings, try to express it in a creative way. Try journaling, painting, drawing, make a mind map of feelings, write letters you do not send or whatever feels right for you. The idea of this exercise is not to make beautiful creations – it is a way to express feelings and does not have to be shared with anyone.  
Maintain hobbies and interests. Keeping a daily living schedule can be difficult when caring for someone with dementia. However, in coping with grief and feelings of loss, keeping a routine can be a good way to cope. Think about what you can do to keep your life as “normal” as possible and seek out for help.  
Look after your physical health. Mental and physical health goes hand in hand. Look after your physical health, both by taking symptoms you might experience from the grief seriously and keep moving and eating regularly and varied.  
Seek professional help if it gets too overwhelming. Talk to your doctor about what you are experiencing. Keep in mind that the person with dementia is depending on your health, where you cannot care for anyone without caring for yourself.