tmux unbind arrow keys

Use unbind-key:

unbind Left
unbind Down
unbind Up
unbind Right

If you want to stick to vim-like navigation, would be useful to remap the resize-pane also:

# vim-like pane resizing  
bind -r C-k resize-pane -U
bind -r C-j resize-pane -D
bind -r C-h resize-pane -L
bind -r C-l resize-pane -R

# vim-like pane switching
bind -r k select-pane -U 
bind -r j select-pane -D 
bind -r h select-pane -L 
bind -r l select-pane -R 

# and now unbind keys
unbind Up     
unbind Down   
unbind Left   
unbind Right  

unbind C-Up   
unbind C-Down 
unbind C-Left 
unbind C-Right

I'll show you my .tmux.conf as an example

And by the way, don't forget to remap the 'horizontal-split' in case you have it on the h key as it will interfere with your pane-resize and pane-switch.