How to make a dedicated Ethernet port on a dual Ethernet supported Linux device, which can work independently from the default port?

In a Cortex-A5 based Linux board, I have connected an external Ethernet through SPI protocol. Now the system has 2 Ethernet port. After modifying the file /etc/network/interfaces, I got 2 different IP. Here eth0 is the internal port and eth1 is the external port. I have made eth0 as the default route.

root@iSense-V4:~# ip route
default via 10.1.1.1 dev eth0 
10.1.1.0/24 dev eth0 proto kernel scope link src 10.1.1.45 
10.1.1.0/24 dev eth1 proto kernel scope link src 10.1.1.46

Both are working fine, but if I remove the cable of the default route port "eth0", none of the IP are becoming unreachable. If I remove the eth1 and connect only eth0 both the IPs are becoming reachable. But I want the eth1 port to work independently from the eth0. Is there any way to do so? Can you please help me with this? Here is a detailed information regarding both the port

root@iSense-V4:~# ethtool eth1
Settings for eth1:
    Supported ports: [ TP ]
    Supported link modes:   10baseT/Half 10baseT/Full 
    Supported pause frame use: No
    Supports auto-negotiation: No
    Advertised link modes:  Not reported
    Advertised pause frame use: No
    Advertised auto-negotiation: No
    Speed: 10Mb/s
    Duplex: Half
    Port: Twisted Pair
    PHYAD: 0
    Transceiver: internal
    Auto-negotiation: off
    MDI-X: Unknown
    Current message level: 0x00000036 (54)
                   probe link ifdown ifup
root@iSense-V4:~# 

root@iSense-V4:~# ethtool eth0
Settings for eth0:
    Supported ports: [ TP MII ]
    Supported link modes:   10baseT/Half 10baseT/Full 
                            100baseT/Half 100baseT/Full 
    Supported pause frame use: No
    Supports auto-negotiation: Yes
    Advertised link modes:  10baseT/Half 10baseT/Full 
                            100baseT/Half 100baseT/Full 
    Advertised pause frame use: No
    Advertised auto-negotiation: Yes
    Link partner advertised link modes:  10baseT/Half 10baseT/Full 
                                         100baseT/Half 100baseT/Full 
    Link partner advertised pause frame use: Symmetric Receive-only
    Link partner advertised auto-negotiation: Yes
    Speed: 100Mb/s
    Duplex: Full
    Port: MII
    PHYAD: 7
    Transceiver: internal
    Auto-negotiation: on
    Link detected: yes
root@iSense-V4:~# 

Here is the network configuration in /etc/network/interfaces

auto eth0 eth1
iface eth0 inet static
    address 10.1.1.45
    netmask 255.255.255.0
    network 10.1.1.0
    gateway 10.1.1.1

iface eth1 inet static
        address 10.1.1.46
        netmask 255.255.255.0
        network 10.1.1.0
        gateway 10.1.1.1